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: 33


To show that the two trapezoids ABCD and DCFE are similar its important to show that their corresponding angles are congruent and their sides are proportional. 1- Its given that $ AB \parallel DC \parallel EF $ •Therefore corresponding angles are congruent. 2- since AD=DE and BC = CF Setting up the proportion $\frac{AD}{DE}=\frac{BC}{CF}=\frac{AB}{DC}$ And $ \frac{AB}{DE}=\frac{BC}{CF}=1 $ but $ \frac{AB}{DC}\ne 1 $ Because its not given that the two transversals are parallel therefore $ AB \ne DC \ne EF $ And the proportionality is false. • Therefore the two trapezoids are not similar.

Work Step by Step

They are similar because the corresponding angles of the parallel lines will show you that all the corresponding angles of the trapezoids are congruent and because the midpoint relationship of the line segments show that they both have congruent bases.
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