Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 8 - Right Triangles and Trigonometry - Get Ready! - Page 487: 5

Answer

The triangles are similar according to the Angle-Angle (AA) Similarity Postulate.

Work Step by Step

The triangles are connected by a pair of vertical angles, which are congruent; therefore, we have one angle congruent in the two triangles. If $CD$ and $AB$ are parallel, alternate interior angles are congruent. This makes $\angle D ≅ \angle A$. So, we have two consecutive angles congruent in both triangles; therefore, the triangles are similar according to the Angle-Angle (AA) Similarity Postulate.
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