Elementary Geometry for College Students (5th Edition)

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

Chapter 3 - Section 3.1 - Congruent Triangles - Exercises: 36

Answer

With the information given, it follows that $\triangle ABC\cong\triangle EDC$, according to method AAS.

Work Step by Step

We are given that - $\angle A\cong\angle E$ - $\overline{BC}\cong\overline{DC}$ We see that $\overline{AD}$ intersects $\overline{BE}$ at $C$. So, $\angle ACB\cong\angle ECD$ We now have 2 angles and a non-included side of $\triangle ABC$ are congruent with 2 corresponding angles and a non-included side of $\triangle EDC$. Therefore, according to method AAS, $\triangle ABC\cong\triangle EDC$.
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