Geometry: Common Core (15th Edition)

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

Chapter 5 - Relationships Within Triangles - 5-7 Inequalities in Two Triangles - Lesson Check - Page 336: 1


$\overline{FD}$ > $\overline{BC}$

Work Step by Step

According to the Hinge Theorem, if two consecutive sides of a triangle are congruent to two consecutive sides in another triangle, but their included angles are not congruent, then the side that is opposite to the larger included angle is longer than the side that is opposite the smaller included angle. $m \angle E$ in $\triangle DEF$ is $75^{\circ}$ whereas $m \angle A$ in $\triangle ABC$ is only $70^{\circ}$; therefore, $\angle E$ is the bigger angle, and the side opposite to it will be the longer side. $\overline{FD}$ > $\overline{BC}$
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