1. 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.

2. 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.

3. 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

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 .

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

6. 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.

7. 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
Find the value of x.
ANSWER 8