Elementary Geometry for College Students (7th Edition) Clone

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

Chapter 6 - Section 6.4 - Some Constructions and Inequalities for the Circle - Exercises - Page 310: 11

Answer

No, they are not similar.

Work Step by Step

The angles of triangle XYZ are equal to half of the arcs XY, YZ, and XZ. Therefore they measure 60$^{\circ}$, 65$^{\circ}$, and 55$^{\circ}$. m$\angle$C=.5(ZX+XY-YZ) m$\angle$C=.5(230-130) m$\angle$C=50$^{\circ}$ Similar triangles have congruent angles. Since m$\angle$C is not equal to the measures of any of the angles in triangle XYZ, the two triangles cannot be similar.
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