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Question
ABC is an isosceles triangle with AB = AC. Drawn AP ⊥ BC to show that ∠B = ∠C.
Solution
Given: ABC is an isosceles triangle
In which AB = AC
To prove: ∠B = ∠C
Construction: Draw AP ⊥ BC.
Proof: In ∆ABP and ∆ACP,
∠APB = ∠APC ...(Each 90°) ...(By construction)
AB = AC ...(Given)
AP = AP ...(Common)
ΔABP ≅ ΔACP ...(By RHS congruence rule)
Hence, ∠B = ∠C ...(Corresponding parts of congruent triangles)
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