Theorem: Angles opposite to two equal sides of a triangle are equal.
Given: A in which To Prove: AB = AC Construction: Draw the bisector of and Let it meet BC at D. Proof: In we have [Given] [By construction] AD = AD [ Common ] So, by AAS criterion of congruence, we have
[C.P.C.T] |
Illustration: Prove that measure of each angle of an equilateral triangle is .
Solution: Let be an equilateral triangle. Then, AB = BC = CA Since angles opposite to equal sides of a triangle are equal. AB = BC and BC = CA and But, [ Angle Sum Property ]
Hence, |
In the following figure, AB = AC, D is the point in the interior of such that . Then which of the following statement is true? | |||
Right Option : A | |||
View Explanation |
In the above figure, if and , then which of the following statement is true? | |||
Right Option : C | |||
View Explanation |
In the above figure, If , then which of the following is true? | |||
Right Option : A | |||
View Explanation |
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