Question

ABC is a triangle in which AB = AC. P is any point in the interior of the triangle such that angle ABP = angle ACP. Prove that AP bisects angle BAC

Answer 1

Given : AB = AC 
∠ABP = ∠ACP 

TO PROVE : ∠BAP = ∠CAP 

Proof: In Δ BAP and ΔCAP 

AP = AP 
AB = AC 
∠ABP = ∠ACP 

so bye SAS rule ΔBAP = Δ CAP 

∴ BY CPCT 

∠BAP = ∠CAP 

⇒ AP bisects ∠BAC 

Answer 2

CRM

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