Question 88808
Here's a way that you can do it, but you will need to refine it a little:
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Statement: line xz congruent to line yz Reason: Given
Statement: line zp bisects line xy Reason: Given
Statement: line xp congruent to line py Reason: definition of bisector
Statement: line zp congruent to line zp Reason: identity
Statement: Triangle xzp congruent to Triangle yzp Reason: SSS congruent to SSS
Statement: Angle xzp congruent to Angle yzp Reason: Corresponding parts of congruent triangles are congruent
Statement: Line zp bisects angle xzp Reason: Definition of angle bisector
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Hope this leads you to an appropriate solution.