Answer
1) Show that $\angle 1\cong\angle 2$.
2) Use method SAS for the following pairs:
- $\overline{MP}\cong\overline{NP}$
- $\overline{PQ}\cong\overline{PQ}$
- $\angle 1\cong\angle 2$
Work Step by Step
Since it is given that $\vec{PQ}$ bisects $\angle MPN$, we can deduce that the angle value of $\angle 1$ is equal with the angle value of $\angle 2$.
So, $\angle 1\cong\angle 2$.
Furthermore, we also have
1) $\overline{MP}\cong\overline{NP}$
2) $\overline{PQ}\cong\overline{PQ}$ (by Identity)
So we have 2 sides and an included angle of $\triangle MQP$ are congruent with 2 sides and an included angle of $\triangle NQP$.
Therefore, according to method SAS, $\triangle MQP\cong\triangle NQP$.
