Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 3 - Section 3.2 - Corresponding Parts of Congruent Triangles - Exercises - Page 137: 11

Answer

Proof for the problem: 1. $\overline{SR}\cong\overline{SV}$ (1. Given) 2. $\overline{RT}\cong\overline{VT}$ (2. Given) 3. $\overline{ST}\cong\overline{ST}$ (3. Identity) 4. $\triangle RST\cong\triangle VST$ (4. SSS)

Work Step by Step

1) First, it is given that $\overline{SR}\cong\overline{SV}$ 2) It is also given that $\overline{RT}\cong\overline{VT}$ 3) By identity, we find that $\overline{ST}\cong\overline{ST}$ Now we see that all 3 sides of $\triangle RST$ are congruent with corresponding 3 sides of $\triangle VST$. So we would use SSS to prove triangles congruent. Now we would construct a proof for the problem: 1. $\overline{SR}\cong\overline{SV}$ (1. Given) 2. $\overline{RT}\cong\overline{VT}$ (2. Given) 3. $\overline{ST}\cong\overline{ST}$ (3. Identity) 4. $\triangle RST\cong\triangle VST$ (4. SSS)
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