Question
ABC is an isosceles triangle with AB = AC. Draw AP $\perp$ BC to show that $\angle$B = $\angle$C.
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Answer
Given: $A B C$ is an isosceles triangle with $A B=A C$.
To Prove: $\angle B =\angle C$
Construction: Draw $A P \perp B C$
Proof: In right triangle APB and right triangle $APC.$
$AB = AC . . . .$ [given]
$AP = AP . . . .$[Common]
$\therefore \triangle APB \cong \triangle APC \ldots[RHS \text { rule] }$
$\therefore \angle ABP=\angle ACP \ldots[\text { c.p.c.t. }] $
$\therefore \angle B=\angle C$
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