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)