Elementary Geometry for College Students (5th Edition)

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

Chapter 3 - Section 3.1 - Congruent Triangles - Exercises: 34


It can follow that $\triangle RTS\cong\triangle RUV$ according to method SAS. (But first, prove $\overline{RS}\cong\overline{RV}$)

Work Step by Step

*STRATEGY: 1) Prove that $\overline{RS}\cong\overline{RV}$ 2) Use method SAS to prove triangles congruent. 1) Prove that $\overline{RS}\cong\overline{RV}$ - Draw a line that goes through $R$ and passes $\overline{SV}$ at $H$ so that $\overline{RH}\bot\overline{SV}$. Now we would try to prove that $\triangle RHS\cong\triangle RHV$ Since $\overline{RH}\bot\overline{SV}$, it follows that $\angle RHS=\angle RHV=90^{\circ}$ So, $\angle RHS\cong\angle RHV$ Furthermore, - $\angle S\cong\angle V$ (given) - $\overline{RH}\cong\overline{RH}$ (by Identity) Therefore, according to method AAS, $\triangle RHS\cong\triangle RHV$ So $\overline{RS}\cong\overline{RV}$ 2) We have $\overline{RS}\cong\overline{RV}$. It is also given that - $\angle S\cong\angle V$ - $\overline{ST}\cong\overline{VU}$ So, according to method SAS, $\triangle RTS\cong\triangle RUV$
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