Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Solve each proportion. = = 1. b = 10 2. y = 8 = = 3. 4. m = 52 30 3 9 = 56 35 y 5 = 1. b = 10 2. y = 8 4 12 p 9 = 56 m 28 26 = 3. 4. m = 52 p = 3

Objective - learn to determine whether figures are similar and to find missing dimensions.

Vocabulary Similar - figures having the same shape, but different size. Corresponding sides of two figures are in the same relative position, and corresponding angles are in the same relative position. Two figures are similar if the lengths of corresponding sides are proportional and the corresponding angles have equal measures.

Example #1: Identifying Similar Figures Which rectangles are similar? Hint: Cross Multiply (think proportions)

Which rectangles are similar? 8 ft A 6 ft B C 5 ft 4 ft 3 ft 2 ft Hint: Cross Multiply (think proportions)

Example 2: Finding Missing Measures A picture 10 in. tall and 14 in. wide is to be scaled to 1.5 in. tall to be displayed on a Web page. How wide should the picture be on the Web page for the two pictures to be similar? Set up a proportion. Let w be the width of the picture on the Web page. width of a picture width on Web page height of picture height on Web page 14 w = 10 1.5 14 ∙ 1.5 = w ∙ 10 Find the cross products. 21 = 10w 10w 10 21 = Divide both sides by 10. 2.1 = w The picture on the Web page should be 2.1 in. wide.

Example 3: Using Equivalent Ratios to Find Missing Dimensions A T-shirt design includes an isosceles triangle with side lengths 4.5 in, 4.5 in., and 6 in. An advertisement shows an enlarged version of the triangle with two sides that are each 3 ft. long. What is the length of the third side of the triangle in the advertisement? 6 in. x ft 4.5 in. 3 ft = Set up a proportion. See if you can get the answer of 4 feet?

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 10 10

Lesson Quiz Use the properties of similar figures to answer each question. 1. A rectangular house is 32 ft wide and 68 ft long. On a blueprint, the width is 8 in. Find the length on the blueprint. 17 in. 2. Karen enlarged a 3 in. wide by 5 in. tall photo into a poster. If the poster is 2.25 ft wide, how tall is it? 3.75 ft 3. Which rectangles are similar? A and B are similar.

Lesson Quiz for Student Response Systems 1. A rectangular garden is 45 ft wide and 70 ft long. On a blueprint, the width is 9 in. Identify the length on the blueprint. A. 7 in. B. 9 in. C. 12 in. D. 14 in. 12 12

Lesson Quiz for Student Response Systems 2. Rob enlarged a 4 in. wide by 7 in. tall picture into a banner. If the banner is 3.5 ft wide, how tall is it? A. 6.05 ft B. 6.125 ft C. 7 ft D. 7.125 ft 13 13

Lesson Quiz for Student Response Systems 3. Which triangles are similar? A. X and Y B. X and Z C. Y and Z D. none X Y Z 14 14