{"id":37739,"date":"2023-08-23T11:35:56","date_gmt":"2023-08-23T17:05:56","guid":{"rendered":"https:\/\/therightmentor.com\/?p=37739"},"modified":"2024-06-13T19:19:58","modified_gmt":"2024-06-13T13:49:58","slug":"lines-and-angles-study","status":"publish","type":"post","link":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/","title":{"rendered":"LINES AND ANGLES | Study"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Click For Contents <\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Pre-Requisires\" >Pre-Requisires<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Lines_And_Angles_Speed_Notes\" >Lines And Angles | Speed Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Basic_terms_and_Definitions\" >Basic terms and Definitions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Study_Tools\" >Study Tools<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Angles\" >Angles<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Types_of_Angles\" >Types of Angles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Complementary_and_Supplementary_Angles\" >Complementary and Supplementary Angles<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Intersecting_Lines_and_Non-intersecting_Lines\" >Intersecting Lines and Non-intersecting Lines<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Pairs_of_Angles_Axioms\" >Pairs of Angles Axioms<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Vertically_opposite_Angles_Theorem\" >Vertically opposite Angles Theorem<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Parallel_Lines_and_a_Transversal\" >Parallel Lines and a Transversal<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Transversal_Axioms\" >Transversal Axioms<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Lines_Parallel_to_the_Same_Line\" >Lines Parallel to the Same Line<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Angle_Sum_Property_of_a_Triangle\" >Angle Sum Property of a Triangle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Dig_Deep\" >Dig Deep<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Sub_%E2%80%93_Topics\" >Sub &#8211; Topics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Chapters_Index\" >Chapters Index<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/#Assessments\" >Assessments<\/a><\/li><\/ul><\/nav><\/div>\n\n<hr class=\"wp-block-separator alignfull has-text-color has-vivid-cyan-blue-color has-alpha-channel-opacity has-vivid-cyan-blue-background-color has-background is-style-wide is-style-wide--1\"\/>\n\n\n\n<div class=\"wp-block-group alignfull has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group alignfull has-tertiary-background-color has-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-19c400f2 wp-block-group-is-layout-constrained\" style=\"margin-top:0;margin-bottom:0\">\n<div class=\"wp-block-buttons alignfull is-content-justification-left is-layout-flex wp-container-core-buttons-is-layout-6e9f73ed wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-base-color has-vivid-red-background-color has-text-color has-background wp-element-button\" href=\"https:\/\/therightmentor.com\/number-systems-assessments\/\">Assess<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-vivid-cyan-blue-background-color has-background wp-element-button\" style=\"border-width:2px\">Interact<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group alignfull has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-columns alignfull is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-tertiary-background-color has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<h2 class=\"wp-block-heading has-large-font-size\"><span class=\"ez-toc-section\" id=\"Pre-Requisires\"><\/span>Pre-Requisires<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-small-font-size\">Test &amp; Enrich<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-100 has-custom-font-size is-style-outline has-small-font-size is-style-outline--2\"><a class=\"wp-block-button__link has-text-align-left wp-element-button\">Pre &#8211; Requisite<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"Lines and Angles\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/j_dGPfxKxYA?list=PLEuUy4TjqFeAOkz9COEMEDiOCqPLFgr-9\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption class=\"wp-element-caption\">English Version<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns alignfull is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-base-background-color has-text-color has-background has-link-color wp-elements-2e43300ccace02ecbe03f1d6b528b9e5 is-layout-flow wp-block-column-is-layout-flow\" style=\"color:#000000;padding-top:2em;padding-right:2em;padding-bottom:2em;padding-left:2em\">\n<h2 class=\"wp-block-heading\" id=\"single\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Lines_And_Angles_Speed_Notes\"><\/span><strong>Lines And Angles | Speed Notes<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-luminous-vivid-orange-color has-text-color has-normal-font-size\" style=\"line-height:1.5\"><strong><strong>Notes For Quick Recap<\/strong><\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Basic_terms_and_Definitions\"><\/span><strong>Basic terms and Definitions<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"312\" height=\"143\" src=\"https:\/\/therightmentor.com\/wp-content\/uploads\/2023\/09\/image-1.png\" alt=\"\" class=\"wp-image-39367\" style=\"width:442px;height:203px\" srcset=\"https:\/\/therightmentor.com\/wp-content\/uploads\/2023\/09\/image-1.png 312w, https:\/\/therightmentor.com\/wp-content\/uploads\/2023\/09\/image-1-300x138.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-group has-medium-font-size is-layout-flow wp-block-group-is-layout-flow\">\n<p>1. <strong>Point<\/strong> &#8211; A Point is that which has no component. It is represented by a dot.<\/p>\n\n\n\n<p>2. <strong>Line<\/strong> &#8211; When we join two distinct points then we get a line. A line has no endpoints; it can be extended on both sides infinitely.<\/p>\n\n\n\n<p>3. <strong>Line Segment Line<\/strong> &#8211; Segment is the part of the line which has two endpoints.<\/p>\n\n\n\n<p>4. <strong>Ray<\/strong> &#8211; Ray is also a part of the line that has only one endpoint and has no end on the other side.<\/p>\n\n\n\n<p>5. <strong>Collinear points<\/strong>: Points lying on the same line are called Collinear Points.<img decoding=\"async\" style=\"width: 400px;\" src=\"https:\/\/lh5.googleusercontent.com\/QBM4PdXjt951e5AEyk1PVlhfv29aULnBgOL2VAy3QUyhKfbj2tP9YyzTkd8M9drEnjP6qwIm0h-ZUHhtrlKWgjgm4Lqda17XZD0b5K04ie0UjWiqi2UbpgKExLbIcpB2AO0tN67sRpXDUGHMBzbUpxSfrwnaZkY\" alt=\"Collinear and Non-collinear points \"><\/p>\n\n\n\n<p>6. <strong>Non-collinear points<\/strong>: Points which do not lie on the same line are called Non-Collinear Points. <strong>(Scroll to continue &#8230;)<\/strong><\/p>\n<\/div>\n\n\n\n<div style=\"height:42px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-css-opacity has-background is-style-wide is-style-wide--3\" style=\"background-color:#000000;color:#000000\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"single\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Study_Tools\"><\/span><strong>Study Tools<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-luminous-vivid-orange-color has-text-color has-normal-font-size\" style=\"line-height:1.5\"><strong>Audio, Visual &amp; Digital Content<\/strong><\/p>\n\n\n                <div class=\"igd igd-shortcode-wrap igd-shortcode-slider\"\n                     data-shortcode-data=\"{"id":232,"status":"on","title":"LINES AND ANGLES | Study","type":"slider","allFolders":false,"folders":[{"id":"1mKHmGLFVvAVXPUu-ywtu22YaYGiemI2P","name":"Lines and Angles.pdf","type":"application\/pdf","size":"630055","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/pdf","thumbnailLink":"https:\/\/lh5.googleusercontent.com\/pP86E1cJ3ZNGlvoRX8NIu4McdPPkrR9Z61tkxPR2NLXa78VbUiu8hKTqvevYaGWdWsAOxrno_Ec5Rq8=s220","webViewLink":"https:\/\/drive.google.com\/file\/d\/1mKHmGLFVvAVXPUu-ywtu22YaYGiemI2P\/view?usp=drivesdk","webContentLink":"https:\/\/drive.google.com\/uc?id=1mKHmGLFVvAVXPUu-ywtu22YaYGiemI2P&export=download","created":"2023-08-29T03:42:41.867Z","updated":"2023-03-17T15:37:05.000Z","description":null,"parents":["1a2TZyy8wtOAcqKe34QNL6kK-st5ahl5i"],"shared":true,"sharedWithMeTime":null,"extension":"pdf","resourceKey":null,"copyRequiresWriterPermission":false,"starred":null,"exportLinks":null,"accountId":"13745142253359366437","permissions":{"canPreview":true,"canDownload":true,"canEdit":false,"canDelete":true,"canTrash":true,"canMove":true,"canRename":true,"canShare":true,"copyRequiresWriterPermission":false,"canChangeCopyRequiresWriterPermission":null,"users":{"14839868887310067358":{"type":"user","role":"writer","domain":null},"12393008518953754506":{"type":"user","role":"writer","domain":null},"10368846457677789243":{"type":"user","role":"writer","domain":null},"13745142253359366437":{"type":"user","role":"owner","domain":null}}},"exportAs":[],"isFolder":false},{"id":"1-3od0hImRpeEqRWy51vGHMV-S8ip7RWy","name":"LINES AND ANGLES","type":"application\/pdf","size":"334568","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/pdf","thumbnailLink":"https:\/\/lh4.googleusercontent.com\/1KVpZQ591HdGrhouUngm2HMKJfOmbqXGIOnG9nC1JHEEPZCBhQN3w_PZDMKLhfZjAUx-uI866pyaB_M=s220","webViewLink":"https:\/\/drive.google.com\/file\/d\/1-3od0hImRpeEqRWy51vGHMV-S8ip7RWy\/view?usp=drivesdk","webContentLink":"https:\/\/drive.google.com\/uc?id=1-3od0hImRpeEqRWy51vGHMV-S8ip7RWy&export=download","created":"2021-06-22T07:47:07.732Z","updated":"2023-01-27T18:37:42.623Z","description":null,"parents":["1keqpYxCAlePmtCa_ixMfkmxsAN9X9WsX"],"shared":true,"sharedWithMeTime":null,"extension":"pdf","resourceKey":null,"copyRequiresWriterPermission":false,"starred":null,"exportLinks":null,"accountId":"13745142253359366437","permissions":{"canPreview":true,"canDownload":true,"canEdit":false,"canDelete":true,"canTrash":true,"canMove":true,"canRename":true,"canShare":true,"copyRequiresWriterPermission":false,"canChangeCopyRequiresWriterPermission":null,"users":{"14839868887310067358":{"type":"user","role":"writer","domain":null},"12393008518953754506":{"type":"user","role":"writer","domain":null},"10368846457677789243":{"type":"user","role":"writer","domain":null},"16235743372950782834":{"type":"group","role":"writer","domain":null},"16265465276400750306":{"type":"group","role":"reader","domain":null},"13745142253359366437":{"type":"user","role":"owner","domain":null}}},"exportAs":[],"isFolder":false},{"id":"1-WjuaTDEnm_bV6KNF-2Hv-8zNVT_roLl","name":"LINES AND ANGLES | NCERT Solutions","type":"application\/pdf","size":"251006","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/pdf","thumbnailLink":"https:\/\/lh4.googleusercontent.com\/vvp9nfrXMzCuezlFhaBHZKXUhI2q8mGKnq7_AZQcO76E491N8hiRh5r-E1ZAXRVGG_HEI2ie2frh-Ys=s220","webViewLink":"https:\/\/drive.google.com\/file\/d\/1-WjuaTDEnm_bV6KNF-2Hv-8zNVT_roLl\/view?usp=drivesdk","webContentLink":"https:\/\/drive.google.com\/uc?id=1-WjuaTDEnm_bV6KNF-2Hv-8zNVT_roLl&export=download","created":"2022-07-01T09:46:37.581Z","updated":"2023-09-02T15:13:49.537Z","description":null,"parents":["1VtJ0N1zpF-4oqGqivqJ7qOHsIyaMck2G"],"shared":true,"sharedWithMeTime":null,"extension":"pdf","resourceKey":null,"copyRequiresWriterPermission":true,"starred":null,"exportLinks":null,"accountId":"13745142253359366437","permissions":{"canPreview":true,"canDownload":true,"canEdit":false,"canDelete":true,"canTrash":true,"canMove":true,"canRename":true,"canShare":true,"copyRequiresWriterPermission":true,"canChangeCopyRequiresWriterPermission":null,"users":{"14839868887310067358":{"type":"user","role":"writer","domain":null},"12393008518953754506":{"type":"user","role":"writer","domain":null},"10368846457677789243":{"type":"user","role":"writer","domain":null},"anyoneWithLink":{"type":"anyone","role":"reader","domain":null},"13745142253359366437":{"type":"user","role":"owner","domain":null}}},"exportAs":[],"isFolder":false},{"id":"1onHEemnXHxfWpr0Ptwm_PeFiEB3nZx39","name":"Lines And Angles.pdf","type":"application\/pdf","size":"387484","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/pdf","thumbnailLink":"https:\/\/lh3.googleusercontent.com\/n16XaaHvUZu6A5sNg0iZ7anwABCklTaxnZ-Ny14Bp5Gs_xNiU3zcRXACZaur9r6r2isRKfNriS5_A4o=s220","webViewLink":"https:\/\/drive.google.com\/file\/d\/1onHEemnXHxfWpr0Ptwm_PeFiEB3nZx39\/view?usp=drivesdk","webContentLink":"https:\/\/drive.google.com\/uc?id=1onHEemnXHxfWpr0Ptwm_PeFiEB3nZx39&export=download","created":"2023-08-29T04:27:47.250Z","updated":"2023-03-17T07:30:51.000Z","description":null,"parents":["1eklrCX64sXSgBdNgJXpHNmAWEIVsGk-j"],"shared":true,"sharedWithMeTime":null,"extension":"pdf","resourceKey":null,"copyRequiresWriterPermission":false,"starred":null,"exportLinks":null,"accountId":"13745142253359366437","permissions":{"canPreview":true,"canDownload":true,"canEdit":false,"canDelete":false,"canTrash":false,"canMove":true,"canRename":true,"canShare":true,"copyRequiresWriterPermission":false,"canChangeCopyRequiresWriterPermission":null,"users":{"14839868887310067358":{"type":"user","role":"writer","domain":null},"13745142253359366437":{"type":"user","role":"writer","domain":null},"10368846457677789243":{"type":"user","role":"writer","domain":null},"12393008518953754506":{"type":"user","role":"owner","domain":null}}},"exportAs":[],"isFolder":false}],"privateFolders":false,"allowExtensions":null,"allowAllExtensions":false,"allowExceptExtensions":null,"allowNames":null,"allowAllNames":false,"allowExceptNames":null,"nameFilterOptions":["files"],"showFiles":true,"showFolders":true,"fileNumbers":"","embedWidth":"100%","embedHeight":"480px","sort":{"sortBy":"name","sortDirection":"asc"},"view":"list","lazyLoad":true,"lazyLoadNumber":100,"maxFileSize":"","minFileSize":"","enableFolderUpload":false,"openNewTab":true,"showUploadLabel":true,"uploadLabelText":"Upload Files","allowEmbedPopout":true,"thumbnailCaption":true,"preview":true,"download":false,"displayFor":"everyone","displayUsers":["everyone"],"displayEveryone":false,"displayExcept":[],"showAccessDeniedMessage":true,"nonce":"5cf0977428","canDelete":false,"rename":false,"upload":false,"newFolder":false,"moveCopy":false,"allowShare":false,"allowSearch":false,"createDoc":false,"edit":false,"copyLink":false,"details":false,"comment":false,"photoProof":false,"filters":{"fileNumbers":"","allowExtensions":"","allowAllExtensions":false,"allowExceptExtensions":"","allowNames":"","allowAllNames":false,"allowExceptNames":"","nameFilterOptions":["files"],"showFiles":true,"showFolders":true},"accounts":{"12393008518953754506":{"id":"12393008518953754506","name":"","email":"","photo":"https:\/\/lh3.googleusercontent.com\/a\/ACg8ocK8uWQ6TsBbJmvsK1f4el0KEIxCOG7GUoKMYWpm0lu4F0oYhbI=s64","storage":{"usage":"16110460874","limit":"16106127360"},"lost":false,"root_id":"0ALJOj97JDAWZUk9PVA","user_id":["admin"],"is_specific_folders":true},"13745142253359366437":{"id":"13745142253359366437","name":"","email":"","photo":"https:\/\/lh3.googleusercontent.com\/a\/ACg8ocJFDO1PJ52Pt6nlASXDZ7GcBNKJFGdzYwS-P8oybSgFRgl95g=s64","storage":{"usage":"5289238677","limit":"32212254720"},"lost":false,"root_id":"0AB4OhBWnqYIuUk9PVA","user_id":["admin"],"is_specific_folders":true,"specific_folders":[{"id":"1kLT5QgtzlZTB4khehCrbNGxuudfRGyzi","accountId":"13745142253359366437","name":"My Folder","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder","description":"","type":"application\/vnd.google-apps.folder","parents":["root"]},{"id":"1CayX4rIYQHa3s5MhnnBafPGGl72fEwpE","accountId":"13745142253359366437","name":"TRM Quizzer","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+43+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1JZC1av4JbIaPGqA5dZ8UZw0xHAGWL58K","accountId":"13745142253359366437","name":"CBSE6 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1fcefZOxAkDy_sixjQZuC3S1L1vF61_pM","accountId":"13745142253359366437","name":"EXEMPLAR Solutions","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1CVKR_-Kzp_ek7_mtVkjFWiodMRfyR8oK","accountId":"13745142253359366437","name":"CBSE6 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1qcc336zuNnooTxxkws2pgEBA0pnpTibx","accountId":"13745142253359366437","name":"CBSE7 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"15op-cldu17M4Gg8mPY8UikCbrBvkS8jR","accountId":"13745142253359366437","name":"CBSE7 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1P7OaA_9rN1fU-7sL8mfuGsK_vcfSGCT-","accountId":"13745142253359366437","name":"CBSE8 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1gV2vYSCjSpJs9i9Wpd_mDlJOJbGJq-Rp","accountId":"13745142253359366437","name":"CBSE8 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"13vbs_GJwBN-rI00YbO0ig6y49kShR7Kb","accountId":"13745142253359366437","name":"CBSE9 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1U8MPm42rcZ7-_2Al7tC4wizgazbs28Mu","accountId":"13745142253359366437","name":"CBSE9 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1g7ltmcRLdt61huLeos_s6XZauUPqWQfG","accountId":"13745142253359366437","name":"CBSE10 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1TB0YUU1_tAjWEjVXEUiqvarJfyXmuxEW","accountId":"13745142253359366437","name":"CBSE10 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1n8ctzYDQZozZLRQ10O8t56FUnTzag5sr","accountId":"13745142253359366437","name":"TGT","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1wDBJRJuQLEuWNlbAUuRySK9gyzyL9Iwl","accountId":"13745142253359366437","name":"Speed Notes","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1jsNBaQob68FzrD-FwH4S6G0Ln5jnKLyc","accountId":"13745142253359366437","name":"MATHEMATICS","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1XdwXrcFVhvzQd8T1eV_hQ3MA2_6D7Wmh","accountId":"13745142253359366437","name":"Full Notes","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1Q3E5opGCGFxuZt4SG8u-mku0d2czA8FH","accountId":"13745142253359366437","name":"6,7,8 Summary PPT ","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1YJhlseRfK5Gc_7jMG_-287SJndnMQB-3","accountId":"13745142253359366437","name":"E-Books","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1SMY0yMeh5n_wXkk6OHjIkc4MweyZDKbm","accountId":"13745142253359366437","name":"CBSE Content Videos Purchased Content","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1FJbmcb8ajxKVntaFGtyUZPRlIRvwvBKU","accountId":"13745142253359366437","name":"Chapter Maps","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1smvx1y0YwTFRWPmNW5M0pgm3iSDXFmxo","accountId":"13745142253359366437","name":"Presentations","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+45+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1i1VGOHFHXfUD3PCj09mVIIXsFPMczYdD","accountId":"13745142253359366437","name":"CBSE 10 SAMPLE PAPERS","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1V_7HPklR8NkGdNNT6Xxrbd25nPFBKKen","accountId":"13745142253359366437","name":"CBSE Chapterwise ","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1VJCho8qaVtwdhZNS_yWUGUXhMMFmTL8o","accountId":"13745142253359366437","name":"CBSE 9 Math Notes","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"14wFJFy8u5IvM1nSOWZuvALXp4jLMqYTU","accountId":"13745142253359366437","name":"TextBook Solutions","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1EWS47uRgucSgRlu3pnsLU2TzvDCCCeXi","accountId":"13745142253359366437","name":"Question Bank","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"12h6wARC9zvf8yQlHaYa5WOFFy2xZjoVx","accountId":"13745142253359366437","name":"Lesson Plan","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1bjUQ9xGoGDRTlp0XU2RvHA_HNKTxVl7z","accountId":"13745142253359366437","name":"CBSE Study Material","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1L83k4A8p4uxijZ-A2Ukk0xo6C_TmVYI-","accountId":"13745142253359366437","name":"CBSE 10 Math Chatperwise Exam Question","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1S001dHYbwtaK5vTeol6UAeu8k_8NTI7u","accountId":"13745142253359366437","name":"Amazing Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1ibZAV06_psVDrXyAOFZoucHXTQGyfMME","accountId":"13745142253359366437","name":"Concept Maps","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1I_J8iclBdhB3_vDZcGZWYPst7Gz6y1Vw","accountId":"13745142253359366437","name":"Learning Objectives","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1Q5ZT14xs3oCV1ZxwGcud-Jc88SBZ78b5","accountId":"13745142253359366437","name":"Pre-requisies","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]}],"is_lost":false},"10368846457677789243":{"id":"10368846457677789243","name":"","email":"","photo":"https:\/\/lh3.googleusercontent.com\/a\/ACg8ocKTpx93BAMS8KY-uaYZgz1gysP5ncUf8tHgtrzFFLlfKMsWomdM=s64","storage":{"usage":"15957944391","limit":"16106127360"},"lost":false,"root_id":"0AFtQsgurbu6UUk9PVA","user_id":["admin"],"is_specific_folders":true}},"account":{"id":"13745142253359366437","name":"AMARNATHREDDY .M","email":"info@therightmentor.com","photo":"https:\/\/lh3.googleusercontent.com\/a\/ACg8ocJFDO1PJ52Pt6nlASXDZ7GcBNKJFGdzYwS-P8oybSgFRgl95g=s64","storage":{"usage":"5289238677","limit":"32212254720"},"lost":false,"root_id":"0AB4OhBWnqYIuUk9PVA","user_id":["admin"],"is_specific_folders":true,"specific_folders":[{"id":"1kLT5QgtzlZTB4khehCrbNGxuudfRGyzi","accountId":"13745142253359366437","name":"My Folder","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder","description":"","type":"application\/vnd.google-apps.folder","parents":["root"]},{"id":"1CayX4rIYQHa3s5MhnnBafPGGl72fEwpE","accountId":"13745142253359366437","name":"TRM Quizzer","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+43+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1JZC1av4JbIaPGqA5dZ8UZw0xHAGWL58K","accountId":"13745142253359366437","name":"CBSE6 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1fcefZOxAkDy_sixjQZuC3S1L1vF61_pM","accountId":"13745142253359366437","name":"EXEMPLAR Solutions","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1CVKR_-Kzp_ek7_mtVkjFWiodMRfyR8oK","accountId":"13745142253359366437","name":"CBSE6 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1qcc336zuNnooTxxkws2pgEBA0pnpTibx","accountId":"13745142253359366437","name":"CBSE7 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"15op-cldu17M4Gg8mPY8UikCbrBvkS8jR","accountId":"13745142253359366437","name":"CBSE7 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1P7OaA_9rN1fU-7sL8mfuGsK_vcfSGCT-","accountId":"13745142253359366437","name":"CBSE8 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1gV2vYSCjSpJs9i9Wpd_mDlJOJbGJq-Rp","accountId":"13745142253359366437","name":"CBSE8 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"13vbs_GJwBN-rI00YbO0ig6y49kShR7Kb","accountId":"13745142253359366437","name":"CBSE9 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1U8MPm42rcZ7-_2Al7tC4wizgazbs28Mu","accountId":"13745142253359366437","name":"CBSE9 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1g7ltmcRLdt61huLeos_s6XZauUPqWQfG","accountId":"13745142253359366437","name":"CBSE10 Math","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1TB0YUU1_tAjWEjVXEUiqvarJfyXmuxEW","accountId":"13745142253359366437","name":"CBSE10 Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1n8ctzYDQZozZLRQ10O8t56FUnTzag5sr","accountId":"13745142253359366437","name":"TGT","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1wDBJRJuQLEuWNlbAUuRySK9gyzyL9Iwl","accountId":"13745142253359366437","name":"Speed Notes","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1jsNBaQob68FzrD-FwH4S6G0Ln5jnKLyc","accountId":"13745142253359366437","name":"MATHEMATICS","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1XdwXrcFVhvzQd8T1eV_hQ3MA2_6D7Wmh","accountId":"13745142253359366437","name":"Full Notes","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1Q3E5opGCGFxuZt4SG8u-mku0d2czA8FH","accountId":"13745142253359366437","name":"6,7,8 Summary PPT ","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1YJhlseRfK5Gc_7jMG_-287SJndnMQB-3","accountId":"13745142253359366437","name":"E-Books","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1SMY0yMeh5n_wXkk6OHjIkc4MweyZDKbm","accountId":"13745142253359366437","name":"CBSE Content Videos Purchased Content","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1FJbmcb8ajxKVntaFGtyUZPRlIRvwvBKU","accountId":"13745142253359366437","name":"Chapter Maps","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1smvx1y0YwTFRWPmNW5M0pgm3iSDXFmxo","accountId":"13745142253359366437","name":"Presentations","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+45+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1i1VGOHFHXfUD3PCj09mVIIXsFPMczYdD","accountId":"13745142253359366437","name":"CBSE 10 SAMPLE PAPERS","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1V_7HPklR8NkGdNNT6Xxrbd25nPFBKKen","accountId":"13745142253359366437","name":"CBSE Chapterwise ","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1VJCho8qaVtwdhZNS_yWUGUXhMMFmTL8o","accountId":"13745142253359366437","name":"CBSE 9 Math Notes","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"14wFJFy8u5IvM1nSOWZuvALXp4jLMqYTU","accountId":"13745142253359366437","name":"TextBook Solutions","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1EWS47uRgucSgRlu3pnsLU2TzvDCCCeXi","accountId":"13745142253359366437","name":"Question Bank","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"12h6wARC9zvf8yQlHaYa5WOFFy2xZjoVx","accountId":"13745142253359366437","name":"Lesson Plan","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1bjUQ9xGoGDRTlp0XU2RvHA_HNKTxVl7z","accountId":"13745142253359366437","name":"CBSE Study Material","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1L83k4A8p4uxijZ-A2Ukk0xo6C_TmVYI-","accountId":"13745142253359366437","name":"CBSE 10 Math Chatperwise Exam Question","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1S001dHYbwtaK5vTeol6UAeu8k_8NTI7u","accountId":"13745142253359366437","name":"Amazing Science","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1ibZAV06_psVDrXyAOFZoucHXTQGyfMME","accountId":"13745142253359366437","name":"Concept Maps","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1I_J8iclBdhB3_vDZcGZWYPst7Gz6y1Vw","accountId":"13745142253359366437","name":"Learning Objectives","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]},{"id":"1Q5ZT14xs3oCV1ZxwGcud-Jc88SBZ78b5","accountId":"13745142253359366437","name":"Pre-requisies","iconLink":"https:\/\/drive-thirdparty.googleusercontent.com\/16\/type\/application\/vnd.google-apps.folder+shared","description":"","type":"application\/vnd.google-apps.folder","parents":["1Y6mpNio7gUm2mtZwxVVLBVA4KDSu-ct5"]}],"is_lost":false}}\"\n                     style=\"--module-width: 100%; --module-height: ;\"\n                ><\/div>\n                \n\n\n\n<div style=\"height:75px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group has-medium-font-size is-layout-flow wp-block-group-is-layout-flow\">\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Angles\"><\/span><strong>Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>When two rays begin from the same endpoint then they form an Angle. The two rays are the arms of the angle and the endpoint is the vertex of the angle.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Types_of_Angles\"><\/span><strong>Types of Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Angle<\/td><td>Notation&nbsp;<\/td><td>Image<\/td><\/tr><tr><td>Acute<\/td><td>An angle which is between 0\u00b0 and 90\u00b0.<\/td><td><br><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/3i2tiwV0LsfhJ2yU6zMIcJ8xNGXzaktZukxkDFDiavlV7EihtUkeapaapW79qMoe26Vbq3XgAzWZ0w1UgDS5puXDA6RRWufAcflz6LwZq3GWGK2NC3PkhyEs4fN6cX3ZyG6lB58LMqatHVfN0LSM2MvQz4IKGB8\" alt=\"Acute Angle\" style=\"width: 100px;\"><\/td><\/tr><tr><td>Right<\/td><td>An angle which is exactly equal to 90\u00b0.<\/td><td><br><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/aJeNMYUmH9Q6oGgb1p7Uw7B2POQP2NzLl5JAGNOGQHr-98upbqTMMPtXlx9fUjlIqBsgk_cySBGEvzRSpiKCsheSHSebeFEZFNb9ZfLuH83GAG3s2FQWw8a4AXJSA0JGtC-IPEhRJV51uj_TKdaQNX_DhCzv9-A\" alt=\"Right Angle\" style=\"width: 100px;\"><\/td><\/tr><tr><td>Obtuse<\/td><td>An angle which is between 90\u00b0 and 180\u00b0.<\/td><td><br><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/p564Tzgla_7eK5L4HjnPXzaRahXgBr9BCQZHOlVsQtu2BgBPl0FSGFNcpgLCTQaU2kKBMSrRqcA00BzcGUoDVcqBtQjx4w36ppN8lWLv48JP2fDIIAYy3NE9Abtj5goEmLlLSFJoFa1knRktUF-K6RhrXqPoHpg\" alt=\"Reflex Angle\" style=\"width: 100px;\"><\/td><\/tr><tr><td>Reflex<\/td><td>An angle which is between 180\u00b0 and 360\u00b0<\/td><td><br><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/LqIPtn7UVsc1LmRikNuYf4sk_bRyry5nR5F7IfMFTqLQefHUk_c67NL_NKD4_j61t6oz9xSg6m0V1pzN-zqvb3__KVJgB3N-KwVTKjJpO_nx749IFhhnlFuFaMc4qmMxDh12a7Z-R7xfQapxvh3SjarTjAlKTnY\" alt=\"Obtuse Angle\" style=\"width: 150px;\"><\/td><\/tr><tr><td>Straight<\/td><td>An angle which is exactly equal to 180\u00b0.<\/td><td><br><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/xxCDGoP38a3TTohB_KCy8hDYF9PPzCqpflebWTnCGG8haiCiwk1NWpSbclQa9FjexTGlR7UmpTIjf7egCoh7UCzewjyq6yWQc9zEmqAgC94li6SwJ4_DefYTVOGtB6yrIpOlIMEtXX6XT04emhJnIz85wnlMGBc\" alt=\"Straight Angle\" style=\"width: 170px;\"><\/td><\/tr><tr><td>Complete<\/td><td>An angle which is exactly equal to 360\u00b0.<\/td><td><br><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/Hm3d12IYW9AUsghc-XKJYiYF9dpkHnQ2cZtc-GJPiW2S1HH1SJ6NwxHN7hX18Y3ZYNE23Zz_DEDJapMw86-gF8eumywk5yWaw6kOo5IyJIo5Xk-s5Y6woXur0SpQOKPpfrgDBABfqKbKiJmCTrD864NNJfc_lBk\" alt=\"Complete Angle\" style=\"width: 170px;\"><\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\"><strong>Types of Angles<\/strong><\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Complementary_and_Supplementary_Angles\"><\/span><strong>Complementary and Supplementary Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Complementary Angles are the different angles whose sum is 90\u00b0.&nbsp;&nbsp;<\/p>\n\n\n\n<p>Complementary Angles are the different angles whose sum is 180\u00b0.<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-4 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"620\" height=\"520\" data-id=\"39358\" src=\"https:\/\/therightmentor.com\/wp-content\/uploads\/2023\/09\/image.png\" alt=\"\" class=\"wp-image-39358\" srcset=\"https:\/\/therightmentor.com\/wp-content\/uploads\/2023\/09\/image.png 620w, https:\/\/therightmentor.com\/wp-content\/uploads\/2023\/09\/image-600x503.png 600w, https:\/\/therightmentor.com\/wp-content\/uploads\/2023\/09\/image-300x252.png 300w\" sizes=\"(max-width: 620px) 100vw, 620px\" \/><\/figure>\n<\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Intersecting_Lines_and_Non-intersecting_Lines\"><\/span><strong>Intersecting Lines and Non-intersecting Lines<\/strong><img decoding=\"async\" width=\"196\" height=\"79\" src=\"https:\/\/lh4.googleusercontent.com\/W_iTeOXDMYA1vPyeuvgmCJ99inPPf9gxEJLOStM3pL5uhCZEY0iOGYkFKFINi1u7S0GLa2T5W-oENIoMkAUtyo69QN381dOcjm-4RJe5KD6gRo1hDzXD6xUp4UMJMFdZ4PeEpR9RkOj7aNgGu-lfA-X8Rilhv-c\" alt=\"Intersecting Lines and Non-intersecting Lines\"><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>There are two ways to draw two lines-<\/p>\n\n\n\n<p>1. The lines which cross each other from a particular point are called Intersecting Lines.<\/p>\n\n\n\n<p>2. The lines which never cross each other at any point are called Non-intersecting Lines. These lines are called Parallel Lines and the common length between two lines is the distance between parallel lines.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Pairs_of_Angles_Axioms\"><\/span><strong>Pairs of Angles Axioms<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/ax687sukeDimqZD870uKK67pKWYFsONiYR4e91N65M-q-bpFn4caa_DMPQpuYPHswccnxabA_Yu56UNyFcojZ77KQIgPw8rZg-Wa-oINwVd6A9zJO_VeWEHNNMtCQs9kolpFWHf2amd9_P4XgmQBOWdSBufe4qc\" alt=\"The sum of two adjacent angles formed by that ray is 180\u00b0\" style=\"width: 450px;\"><\/h2>\n\n\n\n<p>1. If a ray stands on a line, then the sum of two adjacent angles formed by that ray is 180\u00b0.<\/p>\n\n\n\n<p>This shows that the common arm of the two angles is the ray which is standing on a line and the two adjacent angles are the linear pair of the angles. As the sum of two angles is 180\u00b0 so these are supplementary angles too.<\/p>\n\n\n\n<p>2. If the sum of two adjacent angles is 180\u00b0, then the arms which are not common of the angles form a line.<\/p>\n\n\n\n<p>This is the reverse of the first axiom which says that the opposite is also true.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Vertically_opposite_Angles_Theorem\"><\/span><strong>Vertically opposite Angles Theorem<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/t7rrWLsmytecxNh7G3qlYteHVqGfrVxkJ612sjAQMqM2aPivr2s27dqapSsMwaD9mvs95V2u4KqtPsuzPd11H1d--9nL8atCVridL2_iuwj0zMAZABAnuta-Yt1P2I2hmn7VH0KUSDp6xlFa4xqPDNyBor48d0o\" alt=\"Vertically opposite Angles\" style=\"width: 450px;\"><\/h2>\n\n\n\n<p>When two lines intersect each other, then the vertically opposite angles so formed will be equal.<\/p>\n\n\n\n<p>AC and BD are intersecting each other so \u2220AOD = \u2220BOC and \u2220AOB = DOC.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Parallel_Lines_and_a_Transversal\"><\/span><strong>Parallel Lines and a Transversal<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/xaTJK19HwtNK2z4kKChunkFvRJJp1PI-0F3KMnwOVtgxZZnifMFwaCePyh__Vu_IMPafFanqQOWDo6b624GjGOjcN4TCBTZ0-dNDJHCTH30a4DyFe_DnUtGcFNtcff9rUwB_j7UC_Xfvl0ZeKwQDH1DlfdhChMI\" alt=\"Parallel Lines and a Transversal\" style=\"width: 450px;\"><\/h2>\n\n\n\n<p>If a line passes through two distinct lines and intersects them at distant points then this line is called Transversal Line.<\/p>\n\n\n\n<p>Here line \u201cl\u201d is transversal of line m and n.<\/p>\n\n\n\n<p>Exterior Angles &#8211; \u22201, \u22202, \u22207 and \u22208<\/p>\n\n\n\n<p>Interior Angles &#8211; \u22203, \u22204, \u22205 and \u22206<\/p>\n\n\n\n<p>Pairs of angles formed when a transversal intersects two lines-<\/p>\n\n\n\n<p>1.<strong> Corresponding Angles:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220 1 and \u2220 5<\/li>\n\n\n\n<li>\u2220 2 and \u2220 6<\/li>\n\n\n\n<li>\u2220 4 and \u2220 8<\/li>\n\n\n\n<li>\u2220 3 and \u2220 7<\/li>\n<\/ul>\n\n\n\n<p>2. <strong>Alternate Interior Angles:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220 4 and \u2220 6<\/li>\n\n\n\n<li>\u2220 3 and \u2220 5<\/li>\n<\/ul>\n\n\n\n<p>3. Alternate Exterior Angles:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220 1 and \u2220 7<\/li>\n\n\n\n<li>\u2220 2 and \u2220 8<\/li>\n<\/ul>\n\n\n\n<p>4. Interior Angles on the same side of the transversal:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220 4 and \u2220 5<\/li>\n\n\n\n<li>\u2220 3 and \u2220 6<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Transversal_Axioms\"><\/span><strong>Transversal Axioms<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><img decoding=\"async\" style=\"width: 450px;\" src=\"https:\/\/lh4.googleusercontent.com\/xGZsvHlu-J5ZbFIIcatRm-kZXdn6lmetqsVc6hZusaeeJDE8oHfZm7rXCuTulX8wLwchqrBdQSVY6yE9Pwf8O63xuBpQwbIGTxy8-o4Y2rvb4q3Tolwf6Zee5ANNYf0A16B2_mbFYUyKmKTY6iOPMqOK7bLwhAM\" alt=\"Transversal Axioms\"><\/p>\n\n\n\n<p>1. If a transversal intersects two parallel lines, then<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Each pair of corresponding angles will be equal.<\/li>\n\n\n\n<li>Each pair of alternate interior angles will be equal.<\/li>\n\n\n\n<li>Each pair of interior angles on the same side of the transversal will be supplementary.<\/li>\n<\/ul>\n\n\n\n<p>2. If a transversal intersects two lines in such a way that<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Corresponding angles are equal then these two lines will be parallel to each other.<\/li>\n\n\n\n<li>Alternate interior angles are equal then the two lines will be parallel.<\/li>\n\n\n\n<li>Interior angles on the same side of the transversal are supplementary then the two lines will be parallel.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Lines_Parallel_to_the_Same_Line\"><\/span><strong>Lines Parallel to the Same Line<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/YMP8airjyzBmqhI_GV-Na92CfJI2pmidzPLX_86oXaMxFyHnpcHYiDcLQDgYX6yoHxSyFIiMT4u9R7tG_ztOoj6USU6OgGskDJ-N3nnI4zzw4ViWT018sEaD3Wh_JGKXYPzFdMXFxV-QTBIQ6C_dBbLQGZStr_E\" alt=\"Lines Parallel to the Same Line\" style=\"width: 450px;\"><\/h2>\n\n\n\n<p>If two lines are parallel with a common line then these two lines will also be parallel to each other.<\/p>\n\n\n\n<p>As in the above figure if AB \u2225 CD and EF \u2225 CD then AB \u2225 EF.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Angle_Sum_Property_of_a_Triangle\"><\/span><strong>Angle Sum Property of a Triangle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/dVnDmdwgjC88KcmLGt77ZpDoQgkBrNyLJJx4gFIW5g70X7EZG7WJ6R5SHB7bXHa4jzqhEeqxDuX5YeQwbsruFku8B_l90IAQJyW9fj9Ew-SEOKSTkcbUMjcc3AfF2O051L7OdLuGqrhs5RcK6cIp5_uWP8YrOCk\" alt=\"The exterior angle formed is equal to the sum of the two interior opposite angles\" style=\"width: 450px;\"><\/h2>\n\n\n\n<p>1. The sum of the angles of a triangle is 180\u00ba.<\/p>\n\n\n\n<p>\u2220A + \u2220B + \u2220C = 180\u00b0<\/p>\n\n\n\n<p>2. If we produce any side of a triangle, then the exterior angle formed is equal to the sum of the two interior opposite angles.<\/p>\n\n\n\n<p>\u2220BCD = \u2220BAC + \u2220ABC.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-uagb-container uagb-block-fe53acc0 alignfull uagb-is-root-container\"><div class=\"uagb-container-inner-blocks-wrap\">\n<div class=\"wp-block-uagb-container uagb-block-f7936561\">\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"Lines and Angles\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/qGUdnq_LyF0?list=PLEuUy4TjqFeD5d6BcrIIo4dbIbYRHUCkO\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption class=\"wp-element-caption\">Hindi Version<\/figcaption><\/figure>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns alignfull is-layout-flex wp-container-core-columns-is-layout-d2da2050 wp-block-columns-is-layout-flex\" style=\"margin-bottom:0\">\n<div class=\"wp-block-column has-tertiary-background-color has-text-color has-background has-link-color wp-elements-2e5ac2404643eed0228dee617e0c2bd5 is-layout-flow wp-block-column-is-layout-flow\" style=\"color:#000000;padding-top:2em;padding-right:2em;padding-bottom:2em;padding-left:2em\">\n<h2 class=\"wp-block-heading\" id=\"family\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Dig_Deep\"><\/span><strong>Dig Deep<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-luminous-vivid-orange-color has-text-color has-normal-font-size\" style=\"line-height:1.5\"><strong>Topic Level Resources<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide is-style-wide--5\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-d2da2050 wp-block-columns-is-layout-flex\" style=\"margin-bottom:0\">\n<div class=\"wp-block-column has-text-color has-background has-link-color wp-elements-c7db55dbe9ca946a40cc845611f21236 is-layout-flow wp-block-column-is-layout-flow\" style=\"color:#000000;background-color:#c0ebf1;padding-top:2em;padding-right:2em;padding-bottom:2em;padding-left:2em\">\n<h2 class=\"wp-block-heading\" id=\"patron\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Sub_%E2%80%93_Topics\"><\/span><strong>Sub &#8211; Topics<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Select A Topic<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide is-style-wide--6\"\/>\n\n\n\n<p class=\"has-medium-font-size\">Topic: <\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-d2da2050 wp-block-columns-is-layout-flex\" style=\"margin-bottom:0\">\n<div class=\"wp-block-column has-text-color has-background has-link-color has-medium-font-size wp-elements-cbc7d8945c2bc94b3a25d36303f59d82 is-layout-flow wp-block-column-is-layout-flow\" style=\"color:#000000;background-color:#d1d1e1;padding-top:2em;padding-right:2em;padding-bottom:2em;padding-left:2em\">\n<h2 class=\"wp-block-heading\" id=\"family\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Chapters_Index\"><\/span><strong>Chapters Index<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-normal-font-size\" style=\"line-height:1.5\"><strong>Select Another Chapter<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide is-style-wide--7\"\/>\n\n\n[display-posts category=&#8221;CBSE 9 &#8211; Mathematics &#8211; Study &#8211; Premium&#8221; order=&#8221;ASC&#8221; posts_per_page=&#8221;25&#8243;]\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group alignfull has-text-color has-background is-layout-flow wp-block-group-is-layout-flow\" style=\"color:#000000;background-color:#ffffff\">\n<h2 class=\"wp-block-heading has-text-align-center\" id=\"schedule-a-visit\" style=\"font-size:clamp(32.969px, 2.061rem + ((1vw - 3.2px) * 2.552), 59px);px;line-height:1.15\"><span class=\"ez-toc-section\" id=\"Assessments\"><\/span><strong>Assessments<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-small-font-size\" style=\"line-height:.9\"><strong><strong>Personalised Assessments<\/strong><\/strong><\/p>\n\n\n\n<div class=\"wp-block-buttons is-horizontal is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-03627597 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-25 has-custom-font-size has-medium-font-size\"><a class=\"wp-block-button__link has-text-color has-background wp-element-button\" style=\"border-radius:50px;color:#ffffff;background-color:#000000\">Assess<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:64px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-query alignfull is-layout-flow wp-block-query-is-layout-flow\">\n<div class=\"wp-block-group has-tertiary-background-color has-background has-link-color wp-elements-1ffaa6c07b8a8727751827fa0b1b960d is-layout-flow wp-block-group-is-layout-flow\"><\/div>\n<\/div>\n\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<div class='heateorSssClear'><\/div><div  class='heateor_sss_sharing_container heateor_sss_horizontal_sharing' data-heateor-sss-href='https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/'><div class='heateor_sss_sharing_title' style=\"font-weight:bold\" >Share\/Assign<\/div><div class=\"heateor_sss_sharing_ul\"><a aria-label=\"Facebook\" class=\"heateor_sss_facebook\" href=\"https:\/\/www.facebook.com\/sharer\/sharer.php?u=https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F\" title=\"Facebook\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg\" style=\"background-color:#0765FE;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"100%\" viewBox=\"0 0 32 32\"><path fill=\"#fff\" d=\"M28 16c0-6.627-5.373-12-12-12S4 9.373 4 16c0 5.628 3.875 10.35 9.101 11.647v-7.98h-2.474V16H13.1v-1.58c0-4.085 1.849-5.978 5.859-5.978.76 0 2.072.15 2.608.298v3.325c-.283-.03-.775-.045-1.386-.045-1.967 0-2.728.745-2.728 2.683V16h3.92l-.673 3.667h-3.247v8.245C23.395 27.195 28 22.135 28 16Z\"><\/path><\/svg><\/span><\/a><a aria-label=\"Google Classroom\" class=\"heateor_sss_button_google_classroom\" href=\"https:\/\/classroom.google.com\/u\/0\/share?url=https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F\" title=\"Google Classroom\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg heateor_sss_s__default heateor_sss_s_Google_Classroom\" style=\"background-color:#ffc112;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"100%\" viewBox=\"-2 2 36 36\"><g fill=\"#fff\"><path d=\"M22.667 16.667a1.667 1.667 0 1 0 0-3.334 1.667 1.667 0 0 0 0 3.334zM22.333 18c-1.928 0-4 .946-4 2.117v1.217h8v-1.217c0-1.17-2.072-2.117-4-2.117zm-13-1.333a1.668 1.668 0 1 0-.002-3.336 1.668 1.668 0 0 0 .002 3.336zM9.667 18c-1.928 0-4 .946-4 2.117v1.217h8v-1.217c0-1.17-2.072-2.117-4-2.117z\"\/><path d=\"M15.335 15.333A2.332 2.332 0 1 0 13 13a2.333 2.333 0 0 0 2.335 2.333zm.332 1.334c-2.572 0-5.333 1.392-5.333 3.11v1.557H21v-1.556c0-1.72-2.762-3.11-5.333-3.11zm3 10.666h8v2h-8v-2z\"\/><\/g><\/svg><\/span><\/a><a aria-label=\"Whatsapp\" class=\"heateor_sss_whatsapp\" href=\"https:\/\/api.whatsapp.com\/send?text=LINES%20AND%20ANGLES%20%7C%20Study%20https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F\" title=\"Whatsapp\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg\" style=\"background-color:#55eb4c;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"100%\" viewBox=\"-6 -5 40 40\"><path class=\"heateor_sss_svg_stroke heateor_sss_no_fill\" stroke=\"#fff\" stroke-width=\"2\" fill=\"none\" d=\"M 11.579798566743314 24.396926207859085 A 10 10 0 1 0 6.808479557110079 20.73576436351046\"><\/path><path d=\"M 7 19 l -1 6 l 6 -1\" class=\"heateor_sss_no_fill heateor_sss_svg_stroke\" stroke=\"#fff\" stroke-width=\"2\" fill=\"none\"><\/path><path d=\"M 10 10 q -1 8 8 11 c 5 -1 0 -6 -1 -3 q -4 -3 -5 -5 c 4 -2 -1 -5 -1 -4\" fill=\"#fff\"><\/path><\/svg><\/span><\/a><a aria-label=\"Telegram\" class=\"heateor_sss_button_telegram\" href=\"https:\/\/telegram.me\/share\/url?url=https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F&text=LINES%20AND%20ANGLES%20%7C%20Study\" title=\"Telegram\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg heateor_sss_s__default heateor_sss_s_telegram\" style=\"background-color:#3da5f1;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"100%\" viewBox=\"0 0 32 32\"><path fill=\"#fff\" d=\"M25.515 6.896L6.027 14.41c-1.33.534-1.322 1.276-.243 1.606l5 1.56 1.72 5.66c.226.625.115.873.77.873.506 0 .73-.235 1.012-.51l2.43-2.363 5.056 3.734c.93.514 1.602.25 1.834-.863l3.32-15.638c.338-1.363-.52-1.98-1.41-1.577z\"><\/path><\/svg><\/span><\/a><a aria-label=\"Teams\" class=\"heateor_sss_button_teams\" href=\"https:\/\/teams.microsoft.com\/share?href=https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F&msgText=LINES%20AND%20ANGLES%20%7C%20Study\" title=\"Teams\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg heateor_sss_s__default heateor_sss_s_teams\" style=\"background-color:#5059c9;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg width=\"100%\" height=\"100%\" style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 32 32\"><path fill=\"#fff\" d=\"M24.63 12.14a2.63 2.63 0 1 0 0-5.26 2.63 2.63 0 0 0 0 5.26Zm2.25.74h-3.29c.18.34.32.72.32 1.12v7.13c0 .74-.11 1.47-.34 2.14 2.01.36 3.94-.93 4.34-2.93.04-.25.09-.52.09-.76V14c0-.63-.52-1.12-1.12-1.12ZM16.75 4.87a3.515 3.515 0 0 0-3.49 3.87h1.73c1.19 0 2.14.97 2.14 2.14v.97c1.75-.2 3.1-1.69 3.1-3.49a3.48 3.48 0 0 0-3.49-3.49h.01Zm4.86 8.01h-4.48v8.01c0 1.19-.97 2.14-2.14 2.14h-3.94c.04.11.07.25.11.36.11.26.22.52.38.74a6.004 6.004 0 0 0 5.2 2.99c3.31 0 5.98-2.68 5.98-6.01v-7.14c0-.61-.49-1.09-1.12-1.09h.01Z\"><\/path><path fill=\"#fff\" d=\"M15 9.86H4.99c-.56 0-.99.45-.99.99v10.02c0 .56.45.99.99.99h10.02c.56 0 .99-.45.99-.99v-9.99c-.01-.56-.44-1.02-1-1.02Zm-2.02 3.74h-2.23v6.01H9.28V13.6H7.03v-1.49h5.96v1.49h-.02.01Z\"><\/path><\/svg><\/span><\/a><a class=\"heateor_sss_more\" aria-label=\"More\" title=\"More\" rel=\"nofollow noopener\" style=\"font-size: 32px!important;border:0;box-shadow:none;display:inline-block!important;font-size:16px;padding:0 4px;vertical-align: middle;display:inline;\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/\" onclick=\"event.preventDefault()\"><span class=\"heateor_sss_svg\" style=\"background-color:#ee8e2d;width:35px;height:35px;border-radius:999px;display:inline-block!important;opacity:1;float:left;font-size:32px!important;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;display:inline;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box;\" onclick=\"heateorSssMoreSharingPopup(this, 'https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/', 'LINES%20AND%20ANGLES%20%7C%20Study', '' )\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewBox=\"-.3 0 32 32\" version=\"1.1\" width=\"100%\" height=\"100%\" style=\"display:block;border-radius:999px;\" xml:space=\"preserve\"><g><path fill=\"#fff\" d=\"M18 14V8h-4v6H8v4h6v6h4v-6h6v-4h-6z\" fill-rule=\"evenodd\"><\/path><\/g><\/svg><\/span><\/a><\/div><div class=\"heateorSssClear\"><\/div><\/div><div class='heateorSssClear'><\/div><br\/><p>Pre-Requisires Test &amp; Enrich Lines And Angles | Speed Notes Notes For Quick Recap Basic terms and Definitions 1. Point &#8211; A Point is that which has no component. It is represented by a dot. 2. Line &#8211; When we join two distinct points then we get a line. A line has no endpoints; it [&hellip;]<\/p>\n<br\/><div class='heateorSssClear'><\/div><div  class='heateor_sss_sharing_container heateor_sss_horizontal_sharing' data-heateor-sss-href='https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/'><div class='heateor_sss_sharing_title' style=\"font-weight:bold\" >Share\/Assign<\/div><div class=\"heateor_sss_sharing_ul\"><a aria-label=\"Facebook\" class=\"heateor_sss_facebook\" href=\"https:\/\/www.facebook.com\/sharer\/sharer.php?u=https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F\" title=\"Facebook\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg\" style=\"background-color:#0765FE;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"100%\" viewBox=\"0 0 32 32\"><path fill=\"#fff\" d=\"M28 16c0-6.627-5.373-12-12-12S4 9.373 4 16c0 5.628 3.875 10.35 9.101 11.647v-7.98h-2.474V16H13.1v-1.58c0-4.085 1.849-5.978 5.859-5.978.76 0 2.072.15 2.608.298v3.325c-.283-.03-.775-.045-1.386-.045-1.967 0-2.728.745-2.728 2.683V16h3.92l-.673 3.667h-3.247v8.245C23.395 27.195 28 22.135 28 16Z\"><\/path><\/svg><\/span><\/a><a aria-label=\"Google Classroom\" class=\"heateor_sss_button_google_classroom\" href=\"https:\/\/classroom.google.com\/u\/0\/share?url=https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F\" title=\"Google Classroom\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg heateor_sss_s__default heateor_sss_s_Google_Classroom\" style=\"background-color:#ffc112;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"100%\" viewBox=\"-2 2 36 36\"><g fill=\"#fff\"><path d=\"M22.667 16.667a1.667 1.667 0 1 0 0-3.334 1.667 1.667 0 0 0 0 3.334zM22.333 18c-1.928 0-4 .946-4 2.117v1.217h8v-1.217c0-1.17-2.072-2.117-4-2.117zm-13-1.333a1.668 1.668 0 1 0-.002-3.336 1.668 1.668 0 0 0 .002 3.336zM9.667 18c-1.928 0-4 .946-4 2.117v1.217h8v-1.217c0-1.17-2.072-2.117-4-2.117z\"\/><path d=\"M15.335 15.333A2.332 2.332 0 1 0 13 13a2.333 2.333 0 0 0 2.335 2.333zm.332 1.334c-2.572 0-5.333 1.392-5.333 3.11v1.557H21v-1.556c0-1.72-2.762-3.11-5.333-3.11zm3 10.666h8v2h-8v-2z\"\/><\/g><\/svg><\/span><\/a><a aria-label=\"Whatsapp\" class=\"heateor_sss_whatsapp\" href=\"https:\/\/api.whatsapp.com\/send?text=LINES%20AND%20ANGLES%20%7C%20Study%20https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F\" title=\"Whatsapp\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg\" style=\"background-color:#55eb4c;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"100%\" viewBox=\"-6 -5 40 40\"><path class=\"heateor_sss_svg_stroke heateor_sss_no_fill\" stroke=\"#fff\" stroke-width=\"2\" fill=\"none\" d=\"M 11.579798566743314 24.396926207859085 A 10 10 0 1 0 6.808479557110079 20.73576436351046\"><\/path><path d=\"M 7 19 l -1 6 l 6 -1\" class=\"heateor_sss_no_fill heateor_sss_svg_stroke\" stroke=\"#fff\" stroke-width=\"2\" fill=\"none\"><\/path><path d=\"M 10 10 q -1 8 8 11 c 5 -1 0 -6 -1 -3 q -4 -3 -5 -5 c 4 -2 -1 -5 -1 -4\" fill=\"#fff\"><\/path><\/svg><\/span><\/a><a aria-label=\"Telegram\" class=\"heateor_sss_button_telegram\" href=\"https:\/\/telegram.me\/share\/url?url=https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F&text=LINES%20AND%20ANGLES%20%7C%20Study\" title=\"Telegram\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg heateor_sss_s__default heateor_sss_s_telegram\" style=\"background-color:#3da5f1;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"100%\" viewBox=\"0 0 32 32\"><path fill=\"#fff\" d=\"M25.515 6.896L6.027 14.41c-1.33.534-1.322 1.276-.243 1.606l5 1.56 1.72 5.66c.226.625.115.873.77.873.506 0 .73-.235 1.012-.51l2.43-2.363 5.056 3.734c.93.514 1.602.25 1.834-.863l3.32-15.638c.338-1.363-.52-1.98-1.41-1.577z\"><\/path><\/svg><\/span><\/a><a aria-label=\"Teams\" class=\"heateor_sss_button_teams\" href=\"https:\/\/teams.microsoft.com\/share?href=https%3A%2F%2Ftherightmentor.com%2Ftrm-course%2Fhome%2Fcourses%2Fcbse-9-mathematics-study-premium%2Flines-and-angles-study%2F&msgText=LINES%20AND%20ANGLES%20%7C%20Study\" title=\"Teams\" rel=\"nofollow noopener\" target=\"_blank\" style=\"font-size:32px!important;box-shadow:none;display:inline-block;vertical-align:middle\"><span class=\"heateor_sss_svg heateor_sss_s__default heateor_sss_s_teams\" style=\"background-color:#5059c9;width:35px;height:35px;border-radius:999px;display:inline-block;opacity:1;float:left;font-size:32px;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box\"><svg width=\"100%\" height=\"100%\" style=\"display:block;border-radius:999px;\" focusable=\"false\" aria-hidden=\"true\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 32 32\"><path fill=\"#fff\" d=\"M24.63 12.14a2.63 2.63 0 1 0 0-5.26 2.63 2.63 0 0 0 0 5.26Zm2.25.74h-3.29c.18.34.32.72.32 1.12v7.13c0 .74-.11 1.47-.34 2.14 2.01.36 3.94-.93 4.34-2.93.04-.25.09-.52.09-.76V14c0-.63-.52-1.12-1.12-1.12ZM16.75 4.87a3.515 3.515 0 0 0-3.49 3.87h1.73c1.19 0 2.14.97 2.14 2.14v.97c1.75-.2 3.1-1.69 3.1-3.49a3.48 3.48 0 0 0-3.49-3.49h.01Zm4.86 8.01h-4.48v8.01c0 1.19-.97 2.14-2.14 2.14h-3.94c.04.11.07.25.11.36.11.26.22.52.38.74a6.004 6.004 0 0 0 5.2 2.99c3.31 0 5.98-2.68 5.98-6.01v-7.14c0-.61-.49-1.09-1.12-1.09h.01Z\"><\/path><path fill=\"#fff\" d=\"M15 9.86H4.99c-.56 0-.99.45-.99.99v10.02c0 .56.45.99.99.99h10.02c.56 0 .99-.45.99-.99v-9.99c-.01-.56-.44-1.02-1-1.02Zm-2.02 3.74h-2.23v6.01H9.28V13.6H7.03v-1.49h5.96v1.49h-.02.01Z\"><\/path><\/svg><\/span><\/a><a class=\"heateor_sss_more\" aria-label=\"More\" title=\"More\" rel=\"nofollow noopener\" style=\"font-size: 32px!important;border:0;box-shadow:none;display:inline-block!important;font-size:16px;padding:0 4px;vertical-align: middle;display:inline;\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/\" onclick=\"event.preventDefault()\"><span class=\"heateor_sss_svg\" style=\"background-color:#ee8e2d;width:35px;height:35px;border-radius:999px;display:inline-block!important;opacity:1;float:left;font-size:32px!important;box-shadow:none;display:inline-block;font-size:16px;padding:0 4px;vertical-align:middle;display:inline;background-repeat:repeat;overflow:hidden;padding:0;cursor:pointer;box-sizing:content-box;\" onclick=\"heateorSssMoreSharingPopup(this, 'https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/lines-and-angles-study\/', 'LINES%20AND%20ANGLES%20%7C%20Study', '' )\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" viewBox=\"-.3 0 32 32\" version=\"1.1\" width=\"100%\" height=\"100%\" style=\"display:block;border-radius:999px;\" xml:space=\"preserve\"><g><path fill=\"#fff\" d=\"M18 14V8h-4v6H8v4h6v6h4v-6h6v-4h-6z\" fill-rule=\"evenodd\"><\/path><\/g><\/svg><\/span><\/a><\/div><div class=\"heateorSssClear\"><\/div><\/div><div class='heateorSssClear'><\/div>","protected":false},"author":1,"featured_media":25365,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"om_disable_all_campaigns":false,"_uag_custom_page_level_css":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"_joinchat":[],"footnotes":""},"categories":[364],"tags":[107,511,121,512,377,114,109,513,178,370,110],"level":[],"tool":[],"class_list":["post-37739","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-9-mathematics-study-premium","tag-cbse","tag-chapter-video","tag-class-9","tag-exemplar-problems","tag-lines-and-angles","tag-material","tag-mathathematics","tag-ncert-book","tag-ncert-solutions","tag-premium","tag-study"],"acf":[],"jetpack_featured_media_url":"https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268.jpg","uagb_featured_image_src":{"full":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268.jpg",1898,1450,false],"thumbnail":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268-150x150.jpg",150,150,true],"medium":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268-300x229.jpg",300,229,true],"medium_large":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268-768x587.jpg",768,587,true],"large":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268-1024x782.jpg",1024,782,true],"1536x1536":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268-1536x1173.jpg",1536,1173,true],"2048x2048":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-2048x1379.jpg",2048,1379,true],"woocommerce_thumbnail":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268-300x300.jpg",300,300,true],"woocommerce_single":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268-600x458.jpg",600,458,true],"woocommerce_gallery_thumbnail":["https:\/\/therightmentor.com\/wp-content\/uploads\/2022\/12\/Teacher-And-Student-scaled-e1703049941268-100x100.jpg",100,100,true]},"uagb_author_info":{"display_name":"AMARNATHREDDY M","author_link":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/author\/amar2330gmail-com\/"},"uagb_comment_info":0,"uagb_excerpt":"Pre-Requisires Test &amp; Enrich Lines And Angles | Speed Notes Notes For Quick Recap Basic terms and Definitions 1. Point &#8211; A Point is that which has no component. It is represented by a dot. 2. Line &#8211; When we join two distinct points then we get a line. A line has no endpoints; it&hellip;","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/posts\/37739","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/comments?post=37739"}],"version-history":[{"count":1,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/posts\/37739\/revisions"}],"predecessor-version":[{"id":49450,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/posts\/37739\/revisions\/49450"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/media\/25365"}],"wp:attachment":[{"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/media?parent=37739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/categories?post=37739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/tags?post=37739"},{"taxonomy":"level","embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/level?post=37739"},{"taxonomy":"tool","embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/tool?post=37739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}