Elementary Geometry for College Students (5th Edition)

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

Chapter 3 - Section 3.2 - Corresponding Parts of Congruent Triangles - Exercises - Page 142: 4

Answer

Proof for the problem: 1. $\overline{MN}\parallel\overline{QR}$ (1. Given) 2. $\angle M\cong\angle R$ and $\angle N\cong\angle Q$ (2. The corresponding alternate interior angles for 2 parallel lines must be congruent) 3. $\overline{MN}\cong\overline{QR}$ (3. Given) 4. $\triangle MNP\cong\triangle RQP$ (4. ASA)

Work Step by Step

1) First, it is given that $\overline{MN}\parallel\overline{QR}$ Therefore, the corresponding alternate interior angles for $\overline{MN}$ and $\overline{QR}$ must be congruent. That means $\angle M\cong\angle R$ and $\angle N\cong\angle Q$ 2) It is also given that $\overline{MN}\cong\overline{QR}$ Now we see that 2 angles and the included side of $\triangle MNP$ are congruent with 2 corresponding angles and the included side of $\triangle RQP$. So we would use ASA to prove triangles congruent. Now we would construct a proof for the problem: 1. $\overline{MN}\parallel\overline{QR}$ (1. Given) 2. $\angle M\cong\angle R$ and $\angle N\cong\angle Q$ (2. The corresponding alternate interior angles for 2 parallel lines must be congruent) 3. $\overline{MN}\cong\overline{QR}$ (3. Given) 4. $\triangle MNP\cong\triangle RQP$ (4. ASA)
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