lesson menu

Main Idea and New Vocabulary

Key Concept: Similar Figures

Example 1: Identify Similar Figures

Example 2: Find Missing Measures

Example 3: Find Missing Measures

• Solve problems involving similar figures.

• similar figures

• corresponding sides

• corresponding angles

• indirect measurement

Identify Similar Figures

Which rectangle is similar to rectangle FGHI?

Rectangle LMNO

Find the ratios of the corresponding sides to see if they are the same.

Identify Similar Figures

Answer: So, rectangle ABCD is similar to rectangle FGHI.

Not SimilarSimilarNot similar

Rectangle ABCD Rectangle QRST

Which triangle is similar to triangle ABC?

A.

B.

C.

D.

Find Missing Measures

If ΔABC ~ ΔDEF, find the length of .

3x= 4.5(11)Find the cross products.

3x= 49.5 Simplify.

x = 16.5 Divide each side by 3.

Find Missing Measures

Write a proportion.

Answer: The length of is 16.5 centimeters.

Let x represent the length of . Then substitute.

A. 12 cm

B. 8.5 cm

C. 3.5 cm

D. 3 cm

If rectangle ABCD ~ rectangle GHIJ then find the

length of .

Find Missing Measures

PALM TREES At a certain time of day, a cabbage palm tree that is 71 feet high casts a shadow that is 42.6 feet long. At the same time, a nearby flagpole casts a shadow that is 15 feet long. How tall is the flagpole?

71(15) = 42.6x Find the cross products.

1,065= 42.6x Simplify.

25 = x Divide each side by 42.6.

Write a proportion.

Answer: The tree is 25 feet tall.

A. 2 ft

B. 9 ft

C. 18 ft

D. 20 ft

SHADOWS An oak tree that is 30 feet tall casts a shadow that is 10 feet long. At the same time, Joe, who is 6 feet tall also casts a shadow. How long is his shadow?