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Main Idea/Vocabulary polygon similar corresponding parts congruent scale factor Identify similar polygons and find missing measures of similar polygons.

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KC 1 BrainPop: Similar Triangles

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Example 1 Identify Similar Polygons Determine whether triangle DEF is similar to triangle HJK. Explain your reasoning.

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Example 1 Identify Similar Polygons Next, check to see if corresponding sides are proportional. Answer:

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1.A 2.B Example 1 A.yes B.no Determine whether triangle ACB is similar to triangle TRI.

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Example 2 Finding Missing Measures Given that rectangle LMNO ~ rectangle GHIJ, find m. Method 1Write a proportion. The missing measure m is the length of NO. Write a proportion involving NO that relates corresponding sides of the two rectangles.

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Example 2 Finding Missing Measures rectangle GHIJ rectangle LMNO rectangle GHIJ GJ = 2, LO = 3, IJ = 4, and NO = m Find the cross products. Multiply. Divide each side by 2.

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Example 2 Finding Missing Measures The scale factor is the constant of proportionality. Method 2Use the scale factor to write an equation. Find the scale factor from rectangle GHIJ to rectangle LMNO by finding the ratio of corresponding sides with known lengths.

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Example 2 Finding Missing Measures Words Variable Equation

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Example 2 Finding Missing Measures Write the equation. Simplify. Answer: The measure is 6. Multiply each side by

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1.A 2.B 3.C 4.D Example 2 A.12 B.15 C.16 D.18 Given that rectangle ABCD ~ rectangle WXYZ, find m.

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KC 2

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Example 3 A polygon has sides 2.5 times as long as a similar polygon. The smaller polygon has a perimeter of 42 inches. What is the perimeter of the larger polygon? A 16.8 in. B 45 in. C 84 in. D 105 in. Read the Item Since each side of the larger polygon is 2.5 times as long as the corresponding sides of the smaller polygon, the scale factor from the smaller polygon to the larger polygon is

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Example 3 Solve the Item Let x represent the perimeter of the larger polygon. The ratio of the perimeters is equal to the ratio of the sides. Answer: D Find the cross products. Simplify. Scale factor relating sides Multiply. Then divide each side by 2. smaller perimeter larger perimeter

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1.A 2.B 3.C 4.D Example 3 A.22 in. B.34 in. C.72 in. D in. A polygon has sides 3.5 times as long as a similar polygon. The larger polygon has a perimeter of 77 inches. What is the perimeter of the smaller polygon?

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1.A 2.B 3.C 4.D Five Minute Check 1 (over Lesson 4-6) A.3 ways B.12 ways C.6 ways D.9 ways Use the draw a diagram strategy. Daniel wants to display three different pictures in a row on his bedroom wall. How many different ways can he arrange the three pictures?

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1.A 2.B 3.C 4.D Five Minute Check 2 (over Lesson 4-6) A.18 students B.36 students C.54 students D.60 students Use the draw a diagram strategy. The music teacher is arranging students on risers for the spring concert. If she places 6 people in the first row and each additional row has 3 more students in it, how many students will be in the fifth row?

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1.A 2.B 3.C 4.D Five Minute Check 3 (over Lesson 4-6) A.13 minutes B.9 minutes 45 seconds C.6 minutes 30 seconds D.3 minutes 15 seconds Jeanine is filling her wading pool with water. After 3 minutes and 15 seconds, the pool is only full. If the pool can hold 350 gallons of water, how much longer will it take to fill the pool?

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