Main Idea and New Vocabulary Key Concept: Similar Figures Example 1: Identify Similar Figures Example 2: Find Missing Measures Example 3: Find Missing Measures Lesson Menu

Solve problems involving similar figures. corresponding sides corresponding angles indirect measurement Main Idea/Vocabulary

Key Concept

Identify Similar Figures Which rectangle is similar to rectangle FGHI? Example 1

Identify Similar Figures Find the ratios of the corresponding sides to see if they are the same. Rectangle LMNO Rectangle ABCD Rectangle QRST Not Similar Not similar Similar Answer: So, rectangle ABCD is similar to rectangle FGHI. Example 1

Which triangle is similar to triangle ABC? D. Example 1 CYP

If ΔABC ~ ΔDEF, find the length of . Find Missing Measures If ΔABC ~ ΔDEF, find the length of . Example 2

Let x represent the length of . Then substitute. Find Missing Measures Write a proportion. Let x represent the length of . Then substitute. 3x = 4.5(11) Find the cross products. 3x = 49.5 Simplify. x = 16.5 Divide each side by 3. Answer: The length of is 16.5 centimeters. Example 2

If rectangle ABCD ~ rectangle GHIJ then find the length of . A. 12 cm B. 8.5 cm C. 3.5 cm D. 3 cm Example 2 CYP

71(15) = 42.6x Find the cross products. 1,065 = 42.6x Simplify. 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? Write a proportion. 71(15) = 42.6x Find the cross products. 1,065 = 42.6x Simplify. 25 = x Divide each side by 42.6. Answer: The tree is 25 feet tall. Example 3

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? A. 2 ft B. 9 ft C. 18 ft D. 20 ft Example 3 CYP