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: 9

Answer

Proof for the problem: 1. $\angle R$ and $\angle V$ are right $\angle$s. (1. Given) 2. $\angle R\cong\angle V$ (2. Both of these corresponding angles are $90^o$) 3. $\angle 1\cong\angle 2$ (3. Given) 4. $\overline{ST}\cong\overline{ST}$ (4. Identity) 5. $\triangle RST\cong\triangle VST$ (5. AAS)

Work Step by Step

1) First, it is given that $\angle R$ and $\angle V$ are right $\angle$s. Therefore, $\angle R\cong\angle V$ 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 a non-included side of $\triangle RST$ are congruent with 2 corresponding angles and a non-included side of $\triangle VST$. So we would use AAS to prove triangles congruent. Now we would construct a proof for the problem: 1. $\angle R$ and $\angle V$ are right $\angle$s. (1. Given) 2. $\angle R\cong\angle V$ (2. Both of these corresponding angles are $90^o$) 3. $\angle 1\cong\angle 2$ (3. Given) 4. $\overline{ST}\cong\overline{ST}$ (4. Identity) 5. $\triangle RST\cong\triangle VST$ (5. AAS)
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