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 - Review Exercises - Page 177: 3


$\angle$ABE is congruent to $\angle$DEC because of ASA and CPCTC.

Work Step by Step

1.Since it is given that $\overline{AD}$ bisects $\overline{BC}$, we can conclude that $\overline{BE}$ is congruent to $\overline{EC}$. 2.It is given that $\overline{AB}$ $\bot$ $\overline{BC}$ and $\overline{DC} $\bot$ $\overline{BC} so we can prove that $\angle$B and $\angle$C are right angles. 3.$\angle$AEB is congruent to $\angle$CED because of the Vertical Angle Theorem. 4.Now that we have both angles and the side between them we can prove that $\angle$ABE is congruent to $\angle$DEC because of ASA 5.$\overline{AE}$ is congruent to $\overline{EG}$ by CPCTC.
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