{"id":37741,"date":"2023-08-23T11:36:56","date_gmt":"2023-08-23T17:06:56","guid":{"rendered":"https:\/\/therightmentor.com\/?p=37741"},"modified":"2024-06-13T19:19:41","modified_gmt":"2024-06-13T13:49:41","slug":"triangles-study","status":"publish","type":"post","link":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/triangles-study\/","title":{"rendered":"TRIANGLES | 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\/triangles-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\/triangles-study\/#Triangles_Speed_Notes\" >Triangles | 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\/triangles-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-4\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/triangles-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-5\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/triangles-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-6\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/triangles-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-7\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/triangles-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=\"Triangles\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/Wg4Lne7N_aU?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-a3fe019ffdf852b496532e0441bbf089 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=\"Triangles_Speed_Notes\"><\/span><strong>Triangles | 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<div class=\"wp-block-group has-medium-font-size is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Similar Geometric Figures:<\/strong><\/p>\n\n\n\n<p>Two geometric figures which are the same in shape, such that one is simply a copy of the other on a smaller scale or a larger scale, are called <strong>similar geometric figures<\/strong>.<\/p>\n\n\n\n<p>Two geometric figures are said to be similar if and only if they have the same shape but not necessarily the same size. Two congruent geometric figures are always similar but converse may or may not be true. <strong>(Scroll down to read more &#8230;)<\/strong><\/p>\n<\/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\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                     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\"\n                     style=\"--module-width: 100%; --module-height: ;\"\n                ><\/div>\n                \n\n\n\n<div class=\"wp-block-group has-medium-font-size is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Similar Polygons:<\/strong> Two polygons of the same number of sides are similar, if <\/p>\n\n\n\n<p>(i) their corresponding angles are equal and <\/p>\n\n\n\n<p>(ii) their corresponding sides are in proportion or their corresponding sides are in the same ratio. <\/p>\n\n\n\n<p>The same ratio of the corresponding sides is referred to as the representative fraction or the scale factor for the polygons. <\/p>\n\n\n\n<p><strong>Similar Triangles :<\/strong> <\/p>\n\n\n\n<p>Two triangles are said to be similar, <\/p>\n\n\n\n<p>if (i) their corresponding angles are equal and <\/p>\n\n\n\n<p>ii) their corresponding sides are in proportion (are in the same ratio).<\/p>\n\n\n\n<p><strong>Basic Proportionality Theorem (or Thales Theorem) : 1<\/strong><\/p>\n\n\n\n<p>If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio. Or If a line is drawn parallel to one side of a triangle, intersecting the other two sides in distinct points, the other two sides are divided in the same ratio i .e.. If in \u2206ABC, l\u2225 BC, intersecting in D and E. then<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.wixstatic.com\/media\/f69947_909314db1b3e4e61ad4a08e4ea18ee8d~mv2.png\/v1\/fill\/w_652,h_319,al_c,lg_1,q_85,enc_auto\/f69947_909314db1b3e4e61ad4a08e4ea18ee8d~mv2.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Converse of Basic Proportionality Theorem :<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.wixstatic.com\/media\/f69947_6b48e906704f4bfebbdbbdba943b9d41~mv2.png\/v1\/fill\/w_225,h_188,al_c,lg_1,q_85,enc_auto\/f69947_6b48e906704f4bfebbdbbdba943b9d41~mv2.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>If a line divides any two sides of a triangle in the sameratio, the line is parallel to the third side i.e.<\/p>\n\n\n\n<p>In \u2206ABC, if l intersects AB in D and AC in E, such that:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.wixstatic.com\/media\/f69947_10a356cc0de64bd9a4dda8f627d334be~mv2.png\/v1\/fill\/w_191,h_82,al_c,q_85,enc_auto\/f69947_10a356cc0de64bd9a4dda8f627d334be~mv2.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Criteria for Similarity of Triangles:<\/strong><\/p>\n\n\n\n<p>Two triangles are said to be similar, if <\/p>\n\n\n\n<p>(i) their corresponding angles are equal and (ii) their corresponding sides are in proportion (or are in the same ratio). <\/p>\n\n\n\n<p><strong>2 (i) AA or AAA Similarity Criterion :<\/strong> If two angles of one triangle are equal to two corresponding angles of another triangle, then the triangles are similar. If two angles of one triangle are respectively equal to the two angles of another triangle, then the third angles of the two triangles are necessarily equal, because the sum of three angles of a triangle is always 180 <sup>0<\/sup> . <\/p>\n\n\n\n<p><strong>(ii) SAS Similarity Criterion :<\/strong> If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio, then the two triangles are similar. Or If two sides of a triangle are proportional to two corresponding sides of another triangle and the angles included between them are equal, then the triangles are similar.<\/p>\n\n\n\n<p> iii) SSS <strong>Similarity Criterion :<\/strong> If in two triangles, sides of one triangle are proportional (or are in the same ratio) to the sides of the other triangle, then the triangles are similar. If \u2206ABC~ \u2206PQR by any one similarity criterion, then \u2220A=\u2220P, \u2220B=\u2220Q, \u2220C=\u2220R and<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"150\" height=\"55\" src=\"https:\/\/therightmentor.com\/wp-content\/uploads\/2023\/09\/image-4.png\" alt=\"\" class=\"wp-image-39428\"\/><\/figure>\n\n\n\n<p>i.e., A and P, B and Q, C and R are the corresponding vertices, also AB and PQ. BC and QR. CA and RP are the corresponding sides. 3 Areas of <strong>Similar Triangles:<\/strong> The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. &#8211; The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians. &#8211; The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding altitudes. &#8211; The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding angle bisectors. Pythagoras Theorem : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Converse of Pythagoras Theorem : In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and similar to each other i .e ..<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"300\" height=\"238\" src=\"https:\/\/therightmentor.com\/wp-content\/uploads\/2023\/09\/image-3.png\" alt=\"\" class=\"wp-image-39427\"\/><\/figure>\n\n\n\n<p>If in \u2206ABC, \u2220B=90^0 and BD \u22a5 AC, then (i) \u2206ADB ~ \u2206ABC (ii) \u2206BDC ~ \u2206ABC (iii) \u2206ADB ~ \u2206BDC<\/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=\"Volume\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/dy2ZsRQqK0M?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\">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--4\"\/>\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--5\"\/>\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--6\"\/>\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 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Two geometric figures are said to be similar&hellip;","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/posts\/37741","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=37741"}],"version-history":[{"count":1,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/posts\/37741\/revisions"}],"predecessor-version":[{"id":49449,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/posts\/37741\/revisions\/49449"}],"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=37741"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/categories?post=37741"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/tags?post=37741"},{"taxonomy":"level","embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/level?post=37741"},{"taxonomy":"tool","embeddable":true,"href":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/wp-json\/wp\/v2\/tool?post=37741"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}