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 - Page 137: 30


1) Show that $\overline{RM}\cong\overline{RQ}$ 2) Show that $\angle M\cong\angle Q$ 3) Show that $\angle PRQ\cong\angle NRM$ 4) Use method ASA to prove triangles congruent.

Work Step by Step

1) It is given that $\overline{PN}$ bisects $\overline{MQ}$ at R. As a result, $\overline{PN}$ cuts $\overline{MQ}$ into 2 equal parts $\overline{RM}$ and $\overline{RQ}$. Therefore, $\overline{RM}\cong\overline{RQ}$. 2) $\angle M$ and $\angle Q$ are both right angles, so $\angle M\cong\angle Q$. 3) Since $\overline{PN}$ intersects $\overline{MQ}$, $\angle PRQ\cong\angle NRM$. Now we have 2 angles and the included side of $\triangle PRQ$ are congruent with 2 corresponding angles and the included side of $\triangle NRM$. That means according to method ASA, $\triangle PRQ\cong\triangle NRM$.
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