Answer Step-by-step explanation:
I think, using the your angle postulates and line theorems, we can use:
Reflexive property for line CP, saying that it is congruent to itself
Saying that line AP is congruent to line BP by the perpendicular bisector theorem (I think)
Then, when perpendicular lines are formed, a 90 degree angle is formed.
So, if you connected A to C and B to C, you get the triangles, so then you can prove that it was perpendicularly bisected by SAS.
If we say that the perpendicular bisector construction was used, then A would have to be equidistant from P to B
( A_____P_____B )
The lengths that are congruent would be AP and AB (perpendicular bisector theorem), CP congruent to CP (Reflexive property), and AC and BC (CPCTC - Congruent parts of congruent triangles are congruent)