Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 3 - Section 3.1 - Congruent Triangles - Exercises - Page 130: 27


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, $\triangle MQP\cong\triangle NQP$.
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