Geometry: Common Core (15th Edition)

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

Chapter 7 - Similarity - 7-3 Providing Triangles Similar - Practice and Problem-Solving Exercises - Page 455: 11

Answer

One triangle has measures of $35^{\circ}$, $25^{\circ}$, and $120^{\circ}$. The other triangle has measures of $35^{\circ}$, $35^{\circ}$, and $110^{\circ}$. We see that no two angles in one triangle are congruent to any two angles in the other triangle; therefore, these triangles are not similar.

Work Step by Step

We can compare angles in both triangles in this exercise. Let's see if the Angle-Angle Similarity Postulate can be applied here. First, let's look at corresponding angles: $m \angle N ≅ m \angle Y$ because both are $35^{\circ}$. We are not given the measures of another pair of congruent angles, so we will want to find the third angles so we can compare possible corresponding angles. We use the triangle sum theorem, which states that the sum of the measures of the interior angles of a triangle equals $180^{\circ}$. Let's look at $\triangle SUN$: $m \angle U = 180 - (25 + 35)$ Evaluate what is in parentheses first: $m \angle U = 180 - (60)$ Subtract to solve: $m \angle U = 120$ Let's look at $\triangle RAY$: $m \angle R = 180 - (110 + 35)$ Evaluate what is in parentheses first: $m \angle R = 180 - (145)$ Subtract to solve: $m \angle R = 35$ One triangle has measures of $35^{\circ}$, $25^{\circ}$, and $120^{\circ}$. The other triangle has measures of $35^{\circ}$, $35^{\circ}$, and $110^{\circ}$. We see that no two angles in one triangle are congruent to any two angles in the other triangle; therefore, these triangles are not similar.
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