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 - Section 3.1 - Congruent Triangles - Exercises - Page 144: 29


1) Show that $\angle ABC\cong\angle ABD$. 2) Use method SAS for the following pairs: - $\angle ABC\cong\angle ABD$. - $\overline{BC}\cong\overline{BD}$ - $\overline{AB}\cong\overline{AB}$ (by Identity)

Work Step by Step

We have that $\overline{AB}\bot\overline{BC}$ and $\overline{AB}\bot\overline{BD}$ So $\angle ABC$ and $\angle ABD$ are both right angles, which means $\angle ABC\cong\angle ABD$. Furthermore, it is given that - $\overline{BC}\cong\overline{BD}$ - $\overline{AB}\cong\overline{AB}$ (by Identity) Now we have 2 sides and the included angle of $\triangle ABC$ are congruent with 2 corresponding sides and the included angle of $\triangle ABD$. That means according to method SAS, $\triangle ABC\cong\triangle ABD$.
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.