Geometry: Common Core (15th Edition)

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

Chapter 7 - Similarity - Chapter Review - Page 481: 12


$PQR$ ~ $XYZ$ The scale factor is $\frac{3}{2}$ or $3:2$.

Work Step by Step

Let's first identify all the pairs of congruent angles: $\angle P ≅ \angle X$ $\angle Q ≅ \angle Y$ $\angle R ≅ \angle Z$ Now, we can make a similarity statement using the corresponding angles to name the figures: $PQR$ ~ $XYZ$ Now, let's take a look at one set of corresponding sides in both triangles for which we are given values. We can find the scale factor by expressing the lengths of the corresponding sides as a ratio: $\frac{PQ}{XY} = \frac{9}{6}$ Divide the numerator and denominator by their greatest common factor, $3$: $\frac{PQ}{XY} = \frac{3}{2}$ The scale factor is $\frac{3}{2}$ or $3:2$.
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