Geometry: Common Core (15th Edition)

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

Chapter 3 - Parallel and Perpendicular Lines - Common Core Cumulative Standards Review - Selected Response - Page 213: 8



Work Step by Step

An obtuse triangle has an obtuse angle as one of its interior angles. If the sum of all the interior angles in a triangle is $180^{\circ}$, and if one of those angles is more than $90^{\circ}$, then the other two angles must add up to less than $90^{\circ}$. With this in mind, let's take a look at the options given: I. cannot be true because we cannot have a right angle in this triangle when one of the other angles is already greater than $90^{\circ}$. II. is true because each of the two remaining interior angles has to be less than $90^{\circ}$, which is the definition of an acute angle. III. is true because an obtuse triangle must have an obtuse angle in it. IV. cannot be true because a triangle cannot have vertical angles. Therefore, numbers II and III are true. This corresponds to option $G$.
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