Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

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

Answer

1) Show that $\angle PQM\cong\angle PQN$ 2) To prove the triangles congruent, use method ASA for the following pairs: - $\angle PQM\cong\angle PQN$ - $\angle 1\cong\angle 2$ - $\overline{PQ}\cong\overline{PQ}$

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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