Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 3 - Section 3.2 - Corresponding Parts of Congruent Triangles - Exercises - Page 150: 8

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)
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.