Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 3 - Section 3.1 - Congruent Triangles - Exercises - Page 144: 28


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, $\triangle PQM\cong\triangle PQN$.
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