Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 5 - Section 5.2 - Similar Polygons - Exercises - Page 224: 34


Both parallelograms ABCD and DCFE are similar because the two conditions of similarity satisfied. 1- corresponding angles are congruent since segment $AB\parallel DC \parallel EF $. 2- sides are proportional to each other $ \frac{AD}{DE}=\frac{BC}{CF}=\frac{AB}{DC}=1 $ Noting that, since the two transversals are parallel then by theorem the distance between any two parallel lines is the same. Therefore AB= DC = EF.

Work Step by Step

Since the drawing shows the parallelograms have congruent corresponding angles and congruent corresponding sides they are congruent parallelograms and therefore similar to each other.
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