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: 18

Answer

Using method ASA with 2 congruent pairs of angles and a congruent pair of included side, it is proved that $\triangle ABC\cong\triangle DBC$.

Work Step by Step

Since $\angle 1$ and $\angle 2$ are both right angles, it is deduced that $\angle 1\cong\angle 2$. It is also mentioned that - $\overline{AB}\cong\overline{BD}$ - $\angle A\cong\angle D$ We now have 2 angles and the included side of $\triangle ABC$ are congruent with 2 angles and the included side of $\triangle DBC$. Therefore, according to method ASA, $\triangle ABC\cong\triangle DBC$.
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