Geometry: Common Core (15th Edition)

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

Chapter 7 - Similarity - 7-2 Similar Polygons - Practice and Problem-Solving Exercises - Page 444: 9


Congruent angles: $\angle R ≅ \angle D$ $\angle S ≅ \angle E$ $\angle T ≅ \angle F$ $\angle V ≅ \angle G$ Extended proportions: $\frac{RS}{DE} = \frac{ST}{EF} = \frac{TV}{FG} = \frac{VR}{GD}$

Work Step by Step

First, we identify all the pairs of congruent angles: $\angle R ≅ \angle D$ $\angle S ≅ \angle E$ $\angle T ≅ \angle F$ $\angle V ≅ \angle G$ Now, let's take a look at the corresponding sides in both triangles. An extended proportion is given when at least two of the ratios are equal, as they are in similar polygons: $\frac{RS}{DE} = \frac{ST}{EF} = \frac{TV}{FG} = \frac{VR}{GD}$
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