Given:△ABC is isosceles, AB=AC ......(1)
Also,△DBC is isosceles, DB=DC ......(2)
In △ABC and △DBC, we have
AB=AC from (1)
BD=DC from (2)
AD=AD(common)
△ABD≅△ACD(SSS congruence rule)
So, ∠BAP=∠PAC by CPCT ......(1)
In △ABP and △ACP,
AB=AC(given)
∠BAP=∠PAC from (1)
AP=AP(common)
∴△ABP≅△ACP by SAS congruence rule.