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EXAMPLE 2 Find the scale factor Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of ZYXW to FGHJ.

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EXAMPLE 2 Find the scale factor SOLUTION STEP 1 Identify pairs of congruent angles. From the diagram, you can see that Z F, Y G, and X H. Angles W and J are right angles, so W J. So, the corresponding angles are congruent.

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EXAMPLE 2 Find the scale factor SOLUTION STEP 2 Show that corresponding side lengths are proportional. XW HJ ZY FG YX GH WZ JF = = 5 4 = == = = =

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EXAMPLE 2 Find the scale factor SOLUTION The ratios are equal, so the corresponding side lengths are proportional. So ZYXW ~ FGHJ. The scale factor of ZYXW to FGHJ is ANSWER 5 4.

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EXAMPLE 3 Use similar polygons In the diagram, ∆ DEF ~ ∆MNP. Find the value of x. ALGEBRA

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EXAMPLE 3 Use similar polygons Write proportion. Substitute. Cross Products Property Solve for x. SOLUTION The triangles are similar, so the corresponding side lengths are proportional. x = 15 12x = 180 MN DE NP EF = = x

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GUIDED PRACTICE for Examples 2 and 3 In the diagram, ABCD ~ QRST. 2. What is the scale factor of QRST to ABCD ? 1 2 ANSWER 3. Find the value of x. ANSWER 8

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