Explanation:
Given:
AD is the bisector of ∠BAC
∠CPD = ∠BPD
1) ∠CAP = ∠BAP
Reason: definition of angle bisector
2) ∠CPD = 180 − ∠APC, ∠BPD = 180 − ∠APB
Reason: definition of supplementary angles
3) 180 − ∠APC = 180 − ∠APB
Reason: substitution
4) ∠APC = ∠APB
Reason: algebra
5) AP = AP
Reason: reflexive property
6) ΔAPC ≅ ΔAPB
Reason: ASA congruence