Math Help - prove a congruent angle with a bisector

1. prove a congruent angle with a bisector

is this how this is solved?

2. No. Since $\Delta ADP\,\cong \Delta BFP$ then $AP\,=\,PB$.

A bisector divides a segment into two equal lengths and since they are already equal, then $PE\,=\,KP$

EDIT: Your title says prove a congruent angle but your file says prove a side is the same. Is that what you intended?

3. We can call $\measuredangle~ADK=\alpha\implies\measuredangle~KD P=\measuredangle~EFP=\alpha$, and $\measuredangle~KPD=\measuredangle~EPF\implies$ by ASA congruence we have $\triangle{DKP}\cong\triangle{FEP}\implies\overline {PE}=\overline{KP}\,\blacksquare$