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.

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.

EXAMPLE 2 Find the scale factor SOLUTION STEP 2 Show that corresponding side lengths are proportional. ZY FG 25 20 = 5 4 = YX GH 30 24 = 5 4 = XW HJ 15 12 = = 5 4 WZ JF 20 16 = = 5 4

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 .

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

EXAMPLE 3 Use similar polygons SOLUTION The triangles are similar, so the corresponding side lengths are proportional. MN DE NP EF = Write proportion. = 12 9 20 x Substitute. 12x = 180 Cross Products Property x = 15 Solve for x.

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