Warm Up Solve each proportion .

1. 3 9 b 30 = y 5 56 35 = Warm Up Solve each proportion. 1. b = 10 2. y = 8 There are 24 students in Juan’s class. The ratio of girls to boys is 1:2. How many girls and boys are in Juan’s class? 3. 8 girls and 16 boys 4. Three are 32 green and purple markers in a box. The ratio of green markers to purple markers is 3:5. How many of the markers are purple? 20

2. Homework Review

3. Daily Quiz Tim can decorate 3 T-shirts in 20 minutes. How many T-shirts can he decorate in 180 minutes? A company produced blue T-shirts and red T-shirts in the ratio of 22:8. In one hour, the company produced 120 red T-shirts. How many blue T-shirts did the company produce in that hour? 27 330

4. Learn to determine whether figures are similar and to find missing dimensions in similar figures.

5. Corresponding sides& Corresponding angles Sides or angles in the same position on each triangle. Example: p and b r and c q and a Q and A R and C P and B A

6. For two polygons to be similar: Corresponding angles must have the same measures. The ratios of the lengths of the corresponding sides must be proportional.

7. Example of similar figures. Proportions the same. Angles the same. Size NOT the same.

8. New Ferrari V4 Motorcycle Concept designed by Amir Glink Packed with  a modified engine from a Ferrari Enzo! The hand controls are from a F-16 fighter jet Buttons are from a Forumla 1 race car

10. Example 1: Identifying Similar Figures Which rectangles are similar? Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

11. length of rectangle J length of rectangle K 10 5 4 2 width of rectangle J width of rectangle K ? = Additional Example 1 Continued Compare the ratios of corresponding sides to see if they are equal. 20 = 20 The ratios are equal. Rectangle J is similar to rectangle K. The notation J ~ K shows similarity.

12. length of rectangle J length of rectangle L 10 12 4 5 width of rectangle J width of rectangle L ? = Additional Example 1 Continued 50  48 The ratios are not equal. Rectangle J is not similar to rectangle L. Therefore, rectangle K is not similar to rectangle L.

13. Try It: Example 1 Which rectangles are similar? 8 ft A 6 ft B C 5 ft 4 ft 3 ft 2 ft Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

14. length of rectangle A length of rectangle B 8 6 4 3 width of rectangle A width of rectangle B ? = length of rectangle A length of rectangle C 8 5 4 2 width of rectangle A width of rectangle C ? = Check It Out: Example 1 Continued Compare the ratios of corresponding sides to see if they are equal. 24 = 24 The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity. 16  20 The ratios are not equal. Rectangle A is not similar to rectangle C. Therefore, rectangle B is not similar to rectangle C.

15. 14 w 10 1.5 width of a picture width on Web page height of picture height on Web page = 21 10 10w 10 = Additional Example 2: Finding Missing Measures in Similar Figures 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. 14 ∙ 1.5 = w ∙ 10 Find the cross products. 21 = 10w Divide both sides by 10. 2.1 = w The picture on the Web page should be 2.1 in. wide.

16. 56 w 40 10 width of a painting width of poster length of painting length of poster = 560 40 40w 40 = Check It Out: Example 2 A painting 40 in. long and 56 in. wide is to be scaled to 10 in. long to be displayed on a poster. How wide should the painting be on the poster for the two pictures to be similar? Set up a proportion. Let w be the width of the painting on the Poster. 56 ∙ 10 = w ∙ 40 Find the cross products. 560 = 40w Divide both sides by 40. 14 = w The painting displayed on the poster should be 14 in. long.

17. 4.5 in. 3 ft 6 in. x ft = 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? Set up a proportion. 4.5 • x = 3 • 6 Find the cross products.

18. 18 4.5 x = = 4 Additional Example 3 Continued Multiply. 4.5x = 18 Solve for x. The third side of the triangle is 4 ft long.

19. 18 ft 4 in. 24 ft x in. = Check It Out: Example 3 A flag in the shape of an isosceles triangle with side lengths 18 ft, 18 ft, and 24 ft is hanging on a pole outside a campground. A camp t-shirt shows a smaller version of the triangle with two sides that are each 4 in. long. What is the length of the third side of the triangle on the t-shirt? Set up a proportion. 18 • x = 24 • 4 Find the cross products.

20. 96 18 x =  5.3 Check It Out: Example 3 Continued Multiply. 18x = 96 Solve for x. The third side of the triangle is about 5.3 in. long.

21. 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.

22. 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.

23. 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

24. Y X Z 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