Main Idea and New Vocabulary Key Concept Similar

Main Idea and New Vocabulary Key Concept: Similar Polygons Example 1: Identify Similar Polygons Example 2: Find Missing Measures Key Concept: Ratios of Similar Figures Example 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.

Identify Similar Polygons Next, check to see if corresponding sides are proportional. Since , the corresponding sides are proportional. Answer: Therefore, the triangles are similar.

Determine whether the figures are similar. Explain. 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.

Find Missing Measures GEOMETRY Given that rectangle LMNO ~ rectangle GHIJ, find the missing measure. 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 Answer: m = 6 Multiply.

GEOMETRY Given that quadrilateral KLMN ~ quadrilateral RSTU, find the missing measure. A. 6 B. 8 C. 10 D. 12

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.

Find Perimeter Step 2 Find the perimeter of the actual billboard. perimeter of billboard = perimeter of model • scale factor P = 42 • 16 or 672 Substitute. Then simplify. Answer: The perimeter of the actual billboard is 672 inches or 56 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? A. 4 feet B. 4. 5 feet C. 9 feet D. 18 feet