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ΔABC is an isosceles triangle in which AB = AC. Show that ∠B = ∠C.

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ΔABC is an isosceles triangle in which AB = AC. Show that ∠B = ∠C. 

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Given the ΔABC is an isosceles triangle and AB = AC 

Let D be the mid point of BC; Join A, D. 

Now in ΔABD and ΔACD 

AB = AC (given) 

BD = DC (construction) 

AD = AD (common) 

∴ ΔABD ≅ ΔACD (∵ SSS congruence) 

⇒ ∠B = ∠C [∵ CPCT]

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