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 145: 41


1) Prove $\overline{CE}\cong\overline{CB}$ 2) Prove $\angle ACB\cong\angle DCE$ 3) Prove $\angle B\cong\angle E$ 4) Use method ASA to prove triangles congruent.

Work Step by Step

1) It is given that $C$ is the midpoint of $\overline{EB}$. So, $\overline{CE}\cong\overline{CB}$. 2) It is also given that $\overline{AD}\bot\overline{BE}$ So, $\angle ACB=90^{\circ}$ and $\angle DCE=90^{\circ}$ That means $\angle ACB\cong\angle DCE$ 3) We have $\overline{AB}\parallel\overline{ED}$ and $\overline{BE}$ cuts through both $\overline{AB}$ and $\overline{ED}$. Therefore, $\angle B\cong\angle E$ (2 alternate interior angles). 4) From the results in 1), 2) and 3), according to method ASA, $\triangle ABC\cong\triangle DEC$.
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