Geometry: Common Core (15th Edition)

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

Chapter 9 - Transformations - 9-1 Translations - Practice and Problem-Solving Exercises - Page 552: 38



Work Step by Step

In a triangle, the longest side lies opposite the largest angle. With this in mind, we can order the angles in $\triangle PQR$ according to their opposite sides. Let's order the sides from least to greatest first: $\overline{QR} < \overline{PQ} < \overline{RP}$ Now, let's match up the angle with the side opposite to it: $\overline{QR}$ is opposite to $\angle P$ $\overline{PQ}$ is opposite to $\angle R$ $\overline{RP}$ is opposite to $\angle Q$ Option $A$ is not correct. We know nothing about the measures and cannot determine if two angles are less than another angle. Option $B$ is correct. In our lineup, $\angle Q$ is the largest of the three angles. Option $C$ cannot be correct because $m \angle R$ is less than $m \angle Q$ but greater than $m \angle P$. Option $D$ is incorrect. $m \angle P < m \angle R$.
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