Prove that in an Isoceles Triangle angles opposite to the equal sides are equal.
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Given:- ABC is an isoceles triangle.
To prove:- ∠B = ∠C ( Angles opposite to the equal sides of an isoceles triangle)
Construction:- Draw a bisector of ∠A and mark it as D such that AD⊥BC.
Proof:- In ΔBAD & ΔCAD,
AD=AD (common)
AB=AC (given)
∠BAD=∠CAD (by construction)
⇒ ΔBAD≅ΔCAD (by SAS rule)
⇒ ∠ABD=∠ACD (by C.P.C.T)
∴ ∠B= ∠C.
Hence, Proved.
EXPLANATION:
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