Question

Given: NQ is the bisector of ZMNP and ZNMQ
ZNPQ
Prove: Δ MNQ =ΔΡΝΟ
M
N
Q
P

Answer 1

1) $\overline{NQ}$ is the bisector of $\angle MNP$ and $\angle NMQ \cong \angle NPQ$ (given)

2) $\angle MNQ \cong \angle QNP$ (a bisector splits an angle into two congruent angles)

3) $\overline{NQ} \cong \overline{NQ}$ (reflexive property)

4) $\triangle MNQ \cong \triangle PNQ$ (AAS)