ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that B = C.

Given:

In ∆ABC,

AB=BC

AP ⊥ BC

To Prove

 ∠B = ∠C.

Proof

In ∆APB and ∆APC

∠APB = ∠APC —————[ each 90°]

AB=AC ——————-[given]

AP=AP ——————–[common]

∴∆APB ≅ ∆APC ———-[R.H.S]

∠B = ∠C —————[C.P.C.T]

Hence Proved 

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