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Main Idea and New VocabularyKey Concept: Similar Polygons Example 1: Identify Similar PolygonsExample 2: Find Missing MeasuresKey Concept: Ratios of Similar FiguresExample 3: Find Perimeter

• Identify similar polygons and find missing measures of similar polygons.

• similar polygons• corresponding parts• scale factor

Identify Similar Polygons

Determine whether triangle DEF is similar to triangle HJK. Explain.

First, check to see if corresponding angles are congruent.D H, E J, and F K, so all corresponding angles are congruent.

Next, check to see if corresponding sides are proportional.

Identify Similar Polygons

Answer: Therefore, the triangles are similar.

Since , the corresponding sides are

proportional.

A. Yes; corresponding angles are congruent and corresponding sides are proportional.

B. Yes; corresponding angles are congruent and corresponding sides are congruent.

C. No; corresponding angles are congruent, but corresponding sides are not proportional.

D. No; corresponding angles are congruent, but corresponding sides are not congruent.

Determine whether the figures are similar. Explain.

GEOMETRY Given that rectangle LMNO ~ rectangle GHIJ, find the missing measure.

Find Missing Measures

Find the scale factor from rectangle LMNO to rectangle GHIJ.

scale factor:

Find Missing Measures

So, a length on rectangle LMNO is times as long

as the corresponding length on rectangle GHIJ. Let

m represent the measure of ON.

Write the equation.

m = 6 Multiply.

Answer: m = 6

A. 6

B. 8

C. 10

D. 12

GEOMETRY Given that quadrilateral KLMN ~ quadrilateral RSTU, find the missing measure.

Find Perimeter

BILLBOARDS A model of a billboard has a side length of 3 inches. The corresponding side on the actual billboard is 4 feet long. The model has a perimeter of 42 inches. What is the perimeter of the actual billboard?

Step 1 The actual length is proportional to the

length of the model with a ratio of .

Find the scale factor.

Convert feet to inches and divide out units.

Step 2 Find the perimeter of the actual billboard.

P = 42 • 16 or 672 Substitute. Then simplify.

Find Perimeter

Answer: The perimeter of the actual billboard is 672 inches or 56 feet.

perimeter of billboard = perimeter of model • scale factor

A. 4 feet

B. 4.5 feet

C. 9 feet

D. 18 feet

PHOTOGRAPHS A photograph has a side length of 8 inches. The photo is enlarged to poster size and the corresponding side on the poster is 2 feet long. The photograph has a perimeter of 36 inches. What is the perimeter of the poster?