 # 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.

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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.

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 angels, 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. XW HJ ZY FG YX GH WZ JF 25 20 = 15 12 = 5 4 = 20 16 == 5 4 5 4 = = 5 4 30 24 =

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 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 = = 12 9 20 x

GUIDED PRACTICE for Examples 2 and 3 In the diagram, ABCD ~ QRST. SOLUTION STEP 1 Identify pairs of congruent angles. From the diagram, you can see that A = Q, T = D, and B = R. Angles C and S are right angles. So, all the corresponding angles are congruent. 2. What is the scale factor of QRST to ABCD ?

GUIDED PRACTICE for Examples 2 and 3 STEP 2 Show that corresponding side lengths are proportional. QR AB QT AD TS DC RS BC 5 10 = 6 12 = 1 2 = 8 16 = 4 x == 1 2 1 2 =

GUIDED PRACTICE for Examples 2 and 3 The ratios are equal, so the corresponding side lengths are proportional. ANSWER So QRST ~ ABCD. The scale factor of QRST to ABCD 1 2.

GUIDED PRACTICE for Examples 2 and 3 3. Find the value of x. In the diagram, ABCD ~ QRST. Write proportion. Substitute. Cross Products Property Solve for x. SOLUTION The triangles are similar, so the corresponding side lengths are proportional. RS QS BC AC = 4 6 4 + = x 12 x + 4(12 + x) =10 x x = 8

GUIDED PRACTICE for Examples 2 and 3 ANSWER So the value of x is 8

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