angle CPD = angle BPD and AD is the bisector of angle BAC prove that triangle CAP congruent - Maths - Understanding Quadrilaterals

Question

angle CPD = angle BPD and AD is the bisector of angle BAC prove
that triangle CAP congruent to triangle BAP and hence CP=BP

Rajat Sethi · Accepted Answer

for △s CAP and BAPAP=PA ( common side)∠BAP=∠CAP ( as
AD is the angle bisector ∠BAC )∠BPA=∠CPA (as we
have given ∠BPD=∠CPD , ∠BPA=180°-∠BPD and
∠CPA=180°-∠CPD)hence △CAP congruent to
△BAPCP=BP (CPCT)<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/Triangle11%20jpg"
style="width: 435px; height: 289px;">

angle CPD = angle BPD and AD is the bisector of angle BAC . prove that triangle CAP congruent to triangle BAP and hence CP=BP