Elementary Geometry for College Students (6th Edition)

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

Chapter 3 - Section 3.2 - Corresponding Parts of Congruent Triangles - Exercises - Page 138: 30


1) Prove that $\triangle MQP\cong\triangle NPQ$ by method SAS. 2) Then, by CPCTC, $\overline{MP}\cong\overline{NQ}$

Work Step by Step

*PLANNING: - First, prove that $\triangle MQP\cong\triangle NPQ$ - Then, by CPCTC, $\overline{MP}\cong\overline{NQ}$ 1) $\angle MQP$ and $\angle NPQ$ are right $\angle$s. (Given) 2) $\angle MQP\cong\angle NPQ$ (two corresponding right angles are congruent) 3) $\overline{MQ}\cong\overline{NP}$ (Given) 4) $\overline{QP}\cong\overline{PQ}$ (Identity) So now we have 2 lines and the included angle of $\triangle MQP$ are congruent with 2 corresponding lines and the included angle of $\triangle NPQ$ 5) $\triangle MQP\cong\triangle NPQ$ (SAS) 6) $\overline{MP}\cong\overline{NQ}$ (CPCTC)
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