Answer
1) Show that $\angle PQM\cong\angle PQN$
2) To prove the triangles congruent, use method ASA for the following pairs:
Answer Key
1. $\overline{PQ}\bot\overline{MN}$ and $\angle 1\cong\angle 2$ is Given
2. $\angle PQM\cong\angle PQN$; if two lines are $\bot$ they form $\cong$ adj. $\angle$ 's
3. $\overline{PQ}\cong\overline{PQ}$; Identity
4. $\triangle MQP\cong\triangle NQP$; ASA
Work Step by Step
We have that $\overline{PQ}\bot\overline{MN}$.
So $\angle PQM$ and $\angle PQN$ are both right angles, which means $\angle PQM\cong\angle PQN$.
Furthermore, it is given that
- $\angle 1\cong\angle 2$
- $\overline{PQ}\cong\overline{PQ}$
Now we have 2 angles and the included side of $\triangle PQM$ are congruent with 2 corresponding angles and the included side of $\triangle PQN$.
That means according to method ASA, $\triangle PQM\cong\triangle PQN$.
