Elementary Geometry for College Students (5th Edition)

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

Chapter 3 - Review Exercises - Page 172: 3

Answer

$\angle$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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.