Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 5 - Section 5.2 - Similar Polygons - Exercises - Page 235: 20


Both quadrilaterals are parallelograms.

Work Step by Step

Similar figures have congruent corresponding angles. Thus... $m\angle A=m\angle H=70^{\circ}$ $m\angle K=70^{\circ}$ $m\angle B=m\angle J=110^{\circ}$ The interior angles of a quadrilateral will sum to $360^{\circ}$. $360-70-70-110=110$ $m\angle L=110^{\circ}$ A quadrilateral with two sets of congruent opposite angles is a parallelogram. Therefore, quadrilateral HJKL is a parallelogram. Since both quadrilaterals are similar, quadrilateral ABCD is also a parallelogram.
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