Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 3 - Review Exercises - Page 165: 2


$\triangle$DEF is congruent to $\triangle$ABC by SAS and CPCTC.

Work Step by Step

1.It is given the $\overline{EF}$ is congruent to $\overline{AB}$. 2.It is also given that $\overline{DF}$ is congruent to $\overline{AC}$. 3. Since they are vertical angles $\angle$2 is congruent to $\angle$3 by the Vertical Angles Theorem. 4.It is given that $\angle$1 is congruent to $\angle$2. 5. To to number 4 and 5, we can conclude that $\angle$3 is congruent to $\angle$1. 6.Now that we have 2 sides and the angle between them, we can conclude that $\triangle$DEF is congruent to $\triangle$ABC by SAS. 7.Since Corresponding Parts of Congruent Trianles are congruent, $\angle$B is congruent to $\angle$E.
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