Theorem 7.2 : Angles opposite to equal sides of an isosceles triangle are equal.
Given:- Isosceles triangle ABC
To Prove:- ∠B = ∠C
Construction:- Draw the bisector of ∠A and let D be the point of interaction.
⇒In △BAD and △CAD
⇒AB = AC (Given)
⇒∠BAD = ∠CAD (AD is the bisector of ∠A)
⇒AD = AD (Common)
⇒△BAD ⩭ △CAD ( By SAS congruence rule )
⇒∠ABD = ∠ACD (By CPCT)
⇒∠B = ∠C
⇒Hence, angles opposite to equal sides are equal.