You used proportions to solve problems.

• Use proportions to identify similar polygons.

• Solve problems using the properties of similar polygons.

• similar polygons

• scale factor

Use a Similarity Statement

If ΔABC ~ ΔRST, list all pairs of congruent angles and write a proportion that relates the corresponding sides.

Use a Similarity Statement

Use the similarity statement.

ΔABC ~ ΔRST

Congruent Angles: A R, B S, C T

Answer:

If ΔGHK ~ ΔPQR, determine which of the following similarity statements is not true.

A. HGK QPR

B.

C. K R

D. GHK QPR

Use Similar Figures to Find Missing Measures

A. The two polygons are similar. Find x.

Use the congruent angles to write the corresponding vertices in order.

polygon ABCDE ~ polygon RSTUV

Use Similar Figures to Find Missing Measures

Write a proportion to find x.

Similarity proportion

Cross Products Property

Multiply.

Divide each side by 4. Simplify.

Answer: x = __92

Use Similar Figures to Find Missing Measures

B. The two polygons are similar. Find y.

Use the congruent angles to write the corresponding vertices in order.

polygon ABCDE ~ polygon RSTUV

Use Similar Figures to Find Missing Measures

Similarity proportion

Cross Products Property

Multiply.

Subtract 6 from each side.

Divide each side by 6 and simplify.

AB = 6, RS = 4, DE = 8, UV = y + 1

Answer: y = __313

A. a = 1.4

B. a = 3.75

C. a = 2.4

D. a = 2

A. The two polygons are similar. Solve for a.

A. 1.2

B. 2.1

C. 7.2

D. 9.3

B. The two polygons are similar. Solve for b.

Use a Scale Factor to Find Perimeter

If ABCDE ~ RSTUV, find the scale factor of ABCDE to RSTUV and the perimeter of each polygon.

Use a Scale Factor to Find Perimeter

The scale factor ABCDE to RSTUV is or . ___AEVU

__47

Write a proportion to find the length of DC.

Since DC AB and AE DE, the perimeter of ABCDE is 6 + 6 + 6 + 4 + 4 or 26.

Write a proportion.

4(10.5)= 7 ● DC Cross Products Property

6 = DC Divide each side by 7.

Use a Scale Factor to Find Perimeter

Use the perimeter of ABCDE and scale factor to write a proportion. Let x represent the perimeter of RSTUV.

Theorem 7.1

Substitution

4x = (26)(7) Cross Products Property

x = 45.5 Solve.

Use a Scale Factor to Find Perimeter

Answer: The perimeter of ABCDE is 26 and the perimeter of RSTUV is 45.5.

A. LMNOP = 40, VWXYZ = 30

B. LMNOP = 32, VWXYZ = 24

C. LMNOP = 45, VWXYZ = 40

D. LMNOP = 60, VWXYZ = 45

If LMNOP ~ VWXYZ, find the perimeter of each polygon.