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Symmetry | Assess
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Symmetry | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Congruence: The relation of two objects being congruent is called congruence. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Chapter – 7 Congruence of Triangles SSS Congruence of two triangles: Under a given correspondence, two triangles are congruent if the… readmore
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Congruence: The relation of two objects being congruent is called congruence. (Scroll down till end of the page)
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Chapter – 7
Congruence of Triangles
SSS Congruence of two triangles: Under a given correspondence, two triangles are congruent if the three sides of the one are equal to the three corresponding sides of the other.
SAS Congruenceof two triangles: Under a given correspondence, two triangles are
congruent if two sides and the angleincluded between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle.
ASA Congruence of two triangles: Under a given correspondence, two triangles are congruent if two anglesand the side included betweenthem in one of the triangles are equal to the corresponding angles and the side included between them of the other triangle.
RHS Congruence of two right-angled triangles: Under a given correspondence, two right-angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle.
There is no such thing as AAA Congruence of two triangles: Two triangles with equal corresponding angles need not be congruent. In such a correspondence, one of them can be an enlarged copy of the other.
(They would be congruent only if they are exact copies of one another).
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Advanced Tools For Study Assess Interact Symmetry | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Content : (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Content … Key Terms Topic Terminology Term Important Tables Table: . Assessments Test Your Learning readmore
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Advanced Tools For Study Assess Interact WORK AND ENERGY | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Content : (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Content … Key Terms Topic Terminology Term Important Tables Table: . Assessments Test Your Learning readmore
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Advanced Tools For Study Assess Interact Areas Related to Circles | Assess
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Areas Related to Circles | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Introduction : Circumference of a circle Or Perimeter of a circle : The distance around the circle or the length of a circle is called its circumference or perimeter. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Introduction : Circumference… readmore
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Introduction :
Circumference of a circle Or Perimeter of a circle :
The distance around the circle or the length of a circle is called its circumference or perimeter. (Scroll down till end of the page)
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Introduction :
Circumference of a circle Or Perimeter of a circle :
The distance around the circle or the length of a circle is called its circumference or perimeter.
Circumference (perimeter) of a circle = d or 2r, where d is a diameter and r is a radius of the circle and = 227 or 3.14
Area of a circle:
Area of a circle = πr2
Area of a semicircle :
Area of semicircle = 12 πr2
Area of a quadrant :
Area of a quadrant (quarter circle) = r24
Perimeter of a semicircle:
Perimeter of a semicircle or protractor =πr+2r
Area of the ring :
Area of the ring or an annulus
= πR2 – πr2= π(R2 – r2)
= π(R- r)(R+r)
Length of the arc AB
= 2πrθ3600 or πrθ1800
Area of a sector:
Area of sector OACBO =πrθ3600
OR
Area of sector OACBO = 12(r×l)
Perimeter of a sector :
Perimeter of sector OACBO
= Length of arc AB+2r
= πrθ1800+2r
Other important formulae :
(i) Distance moved by a wheel in 1 revolution = Circumference of the wheel.
(ii) Number of revolutions in one minute = Distance moved in 1 minuteCircumference
(iii) Angle described by minute hand in 60 minutes =3600
(iv) Angle described by hour hand in 12 hours = 3600
The midpoint of the hypotenuse of a right triangle is equidistant from the vertices of the triangle.
Angle subtended at the circumference by a diameter is always a right angle.
Area of a segment:
(i) Area of minor segment ACBA
= Area of sector OACBO- Area of ∆OAB
= πrθ3600- 12r2sinθ
(ii) Area of major segment BDAB
= Area of the circle – Area of minor segment ACBA
=πr2 – Area of minor segment ACBA
If a chord subtends a right angle at the center, then
Area of the corresponding segment = 4-12r2
If a chord subtends an angle of 600 at the center, then
Area of the corresponding segment = 6-32r2
If a chord subtends an angle of 1200 at the center, then Area of the corresponding segment = 3-34r2
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Advanced Tools For Study Assess Interact CHEMICAL EFFECTS OF ELECTRIC CURRENT | Assess
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CHEMICAL EFFECTS OF ELECTRIC CURRENT | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Materials through which electric current can pass through easily are called electric conductors or conductors of electricity. Electrical conductivity Or Electric Conductivity: Electrical conductivity is a measure of the ability of a substance to allow the flow of electric current. Among solids metals and graphite are… readmore
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Materials through which electric current can pass through easily are called electric conductors or conductors of electricity.
Electrical conductivity Or Electric Conductivity: Electrical conductivity is a measure of the ability of a substance to allow the flow of electric current.
Among solids metals and graphite are good conductors which have high electrical conductivity.
Some liquids are also good conductors. (Scroll down till end of the page)
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Pure water or distilled water is a poor conductor of electricity. But the presence of even small amount of impurities(salts and minerals) makes water a good conductor as it contains ions through which conduction takes place.
Hence water from taps, wells, lakes, etc. conduct electricity as they contain impurities.
Most liquids that conduct electricity are solutions of acids, bases and salts.
When electricity is passed through a conducting solution, the molecules of the solution dissociate into ions.
Ions are atoms or group of atoms with a positive or a negative charge.
These ions cause electrical conduction through the liquid.
Electrolyte: A liquid That conducts electricity is called an electrolyte.
Electrolysis:
The process of chemical decomposition compound in a solution when an electric current passes through it is called electrolysis.Electrolysis, is due to the chemical effect of electric current.
electrolytic cell: Two electrodes are inserted in the solution and are connected to the terminals of a battery with a switch in between them.
This arrangement is called an electrolytic cell.
anode: The electrode that is connected to the positive terminal of the battery is called the anode,
cathode: The electrode that is connected to the negative terminal of the battery is called the cathode.
Electrolysis is used in refining, electroplating and extraction of metals from impure samples.
electrorefining: This process of refining and extraction of metals from impure samples is called electrorefining.
electroplating: electroplating is the process of coating a useful metal with another metal.
chemical effect of electric current: The process of passing an electric current through a conducting solution to cause chemical reactions is known as the chemical effect of electric current.
Chemical effects of electric current:
(i) Formation of bubbles of a gas on the electrodes.(ii) Deposition of metal on electrodes.
(iii) Change in colour of solutions.
Electroplating: The process of depositing a layer of any desired metal on another material by means of electricity is called electroplating. The object to be electroplated is made the cathode (negative electrode) by connecting it to thenegative terminal of the battery.The metal which has to be deposited is made the anode (positive electrode) by connecting it to the positive terminal of the battery. Usually a salt solution of the metal to be coated is made as anode.
Application of Electroplating:
(i) Metals that rust are often coated with other metals to prevent rusting.(ii) Chromium plating is found on bath taps, car bumpers, etc. to give a bright attractive appearance and resist scratches and wear.
(iii) Silver plating is done on cutlery and jewellery items.
(iv) Tin cans, used for storing food, are made by electroplating tin onto iron.
Tin is less reactive than iron. Thus, food does not come into contact with iron and is protected from getting spoilt.
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= πR2 – πr2
