Theorem 7.2 : Angles opposite to equal sides of an isosceles triangle are equal Class 9

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.

Proof: 

⇒In △BAD and △CAD

⇒AB = AC (Given)

⇒∠BAD = ∠CAD (AD is the bisector of ∠A)

⇒AD = AD (Common)

⇒△BAD ⩭ △CAD ( By SAS congruence rule )

⇒Then, 

⇒∠ABD = ∠ACD (By CPCT)

⇒∠B = ∠C

⇒Hence, angles opposite to equal sides are equal.

⇒Hence proved,

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Theorem 8.9 : The line segment joining the mid-points of two sides of a triangle is parallel to the third side Class 9

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