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