Question

prove that angles opposite to two equal sides of a triangle are equal
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Answer 1

Given: ∆ABC in which ∠B = ∠C

To Prove: AB = AC

Construction: We draw the bisector of ∠A which meets BC in D.

Proof: In ∆ABD and ∆ACD we have ∠B = ∠C

[Given] ∠BAD = ∠CAD [∵AD is bisector of ∠A]

AD = AD [Common side]

∴ By AAS criterion of congruence, we get ∆ABD ≅

∆ACD ⇒ AB = AC

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