Question

Show that in an isosceles triangle, angles opposite to the equal sides are equal.

Answer 1

Hint:- Before solving this question, let us know about Isosceles triangle and its properties.
ISOSCELES TRIANGLE: An isosceles triangle is a triangle in which any two sides are of the equal length.
ISOSCELES TRIANGLE PROPERTIES:-
An isosceles triangle has two congruent sides, which means that two of its sides are of equal length. Also, it has two congruent angles, which means that two of its angles are of the same measure.
The congruent angles of an isosceles triangle are called the base angles while the third angle is known as the vertex angle.

Complete step-by-step solution -
Take a triangle, say ABC, in which AB = AC.
Construct AP bisector of angle ‘A’ meeting BC at ‘P’.

In ∆ABP and ∆ACP
AP = AP (Common)
AB = AC (Given)
Angle BAP = angle CAP (By construction)
Therefore, ∆ABP ≌ ∆ACP (By S.A.S congruence rule)
Therefore, angle ABP = angle ACP (C.P.C.T)
Hence, proved

Note:-Let us now know about C.P.C.T.
C.P.C.T.: C.P.C.T. stands for ‘Corresponding parts of congruent triangles’.
C.P.C.T. the theorem states that if two or more triangles that are congruent to each other are taken then the corresponding angles and the sides of the triangles are also congruent to each other.