**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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