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: 6

Answer

Proof for the problem: 1. $\angle 3\cong\angle 4$ (1. Given) 2. $\angle 1\cong\angle 2$ (2. Given) 3. $\overline{ST}\cong\overline{ST}$ (3. Identity) 4. $\triangle RST\cong\triangle VST$ (4. ASA)

Work Step by Step

1) First, it is given that $\angle 3\cong\angle 4$ 2) It is also given that $\angle 1\cong\angle 2$ 3) By identity, we find that $\overline{ST}\cong\overline{ST}$ Now we see that 2 angles and the included side of $\triangle RST$ are congruent with 2 corresponding angles and the included side of $\triangle VST$. So we would use ASA to prove triangles congruent. Now we would construct a proof for the problem: 1. $\angle 3\cong\angle 4$ (1. Given) 2. $\angle 1\cong\angle 2$ (2. Given) 3. $\overline{ST}\cong\overline{ST}$ (3. Identity) 4. $\triangle RST\cong\triangle VST$ (4. ASA)
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