Question

In the given figure AD is bisector of angle BAC and angle CPD= angle BPD. Prove that triangle CAP congruent triangle BAP and CP= BP.

Answer 1

For triangles CAP and BAP,
AP = PA (common side)
∠ BAP = ∠ CAP (AD is the angle bisector of ∠ BAC)
→ ∠ BPA = ∠ CPA (as we have given ∠ BPD = ∠ CPD, ∠ BPA = 180⁰ - ∠ BPD and ∠ CPA = 180⁰ - ∠ CPD)
Hence Δ CAP congruent to Δ BAP
CP = BP (CPCT).

Answer 2

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