1. Ch. 7 Learning Goal: Ratios & Proportions Learn to find equivalent ratios to create proportions (7-1) Learn to work with rates and ratios (7-2) Learn to use one or more conversion factors to solve rate problems (7-3) Learn to solve proportions (7-4) Learn to identify and create dilations of plane figures (7-5) Learn to determine whether figures are similar, to use scale factors, and to find missing dimensions similar figures (7-6) Learn to make comparisons between and find dimensions of scale drawings and actual objects (7-7) Learn to make comparisons between and find dimensions of scale models and actual objects (7-8) Learn to make scale models of solid figures (7-9)

2. Page 364 #7-12 & #20-24 (SR)

3. Pre-Algebra 7-6 Similar Figures Pre-Algebra Homework Page 370-371 #1-6 & #21-26 (Spiral Review)

4. Pre-Algebra 7-6 Similar Figures 7-6 Similar Figures Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

5. Pre-Algebra 7-6 Similar Figures Warm Up Solve each proportion. Pre-Algebra 7-6 Similar Figures b 30 3939 = 1. 56 35 y5y5 = 2. 4 12 p9p9 = 3. 56 m 28 26 = 4. b = 10y = 8 p = 3 m = 52

6. Pre-Algebra 7-6 Similar Figures Problem of the Day A plane figure is dilated and gets 50% larger. What scale factor should you use to dilate the figure back to its original size? (Hint: The answer is not ). 1212 2323

7. Pre-Algebra 7-6 Similar Figures Today’s Learning Goal Assignment Learn to determine whether figures are similar, to use scale factors, and to find missing dimensions in similar figures.

8. Pre-Algebra 7-6 Similar Figures Vocabulary similar

9. Pre-Algebra 7-6 Similar Figures The heights of letters in newspapers and on billboards are measured using points and picas. There are 12 points in 1 pica and 6 picas in one inch. A letter 36 inches tall on a billboard would be 216 picas, or 2592 points. The first letter in this paragraph is 12 points.

10. Pre-Algebra 7-6 Similar Figures Congruent figures have the same size and shape. Similar figures have the same shape, but not necessarily the same size. The A’s in the table are similar. They have the same shape, but they are not the same size. The ratio formed by the corresponding sides is the scale factor.

11. Pre-Algebra 7-6 Similar Figures Additional Example 1: Using Scale Factors to Find Missing Dimensions 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? To find the scale factor, divide the known measurement of the scaled picture by the corresponding measurement of the original picture. 0.15 1.5 10 = Then multiply the width of the original picture by the scale factor. 2.114 0.15 = 2.1 The picture should be 2.1 in. wide.

12. Pre-Algebra 7-6 Similar Figures Try This: Example 1 A painting 40 in. tall and 56 in. wide is to be scaled to 10 in. tall to be displayed on a poster. How wide should the painting be on the poster for the two pictures to be similar? To find the scale factor, divide the known measurement of the scaled painting by the corresponding measurement of the original painting. 0.25 10 40 = Then multiply the width of the original painting by the scale factor. 1456 0.25 = 14 The painting should be 14 in. wide.

13. Pre-Algebra 7-6 Similar Figures Additional Example 2: 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? Set up a proportion. 6 in. x ft 4.5 in. 3 ft = 4.5 in. x ft = 3 ft 6 in. Find the cross products. 4.5 in. x ft = 3 ft 6 in. in. ft is on both sides

14. Pre-Algebra 7-6 Similar Figures 4.5x = 3 6 4.5x = 18 x = = 4 18 4.5 Cancel the units. Multiply Solve for x. Additional Example 2 Continued The third side of the triangle is 4 ft long.

15. Pre-Algebra 7-6 Similar Figures Try This: Example 2 Set up a proportion. 24 ft x in. 18 ft 4 in. = 18 ft x in. = 24 ft 4 in. Find the cross products. 18 ft x in. = 24 ft 4 in. in ft is on both sides 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?

16. Pre-Algebra 7-6 Similar Figures 18x = 24 4 18x = 96 x =  5.3 96 18 Cancel the units. Multiply Solve for x. Try This: Example 2 Continued The third side of the triangle is about 5.3 in. long.

17. Pre-Algebra 7-6 Similar Figures The following are matching, or corresponding: A and X Remember! AB and XY BC and YZ AC and XZ A CB Z Y X C and Z B and Y

18. Pre-Algebra 7-6 Similar Figures Additional Example 3: 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.

19. Pre-Algebra 7-6 Similar Figures Additional Example 3 Continued 50  48 The ratios are equal. Rectangle J is similar to rectangle K. The notation J ~ K shows similarity. The ratios are not equal. Rectangle J is not similar to rectangle L. 20 = 20 length of rectangle J length of rectangle K width of rectangle J width of rectangle K 10 5 4242 ? = length of rectangle J length of rectangle L width of rectangle J width of rectangle L 10 12 4545 ? = Compare the ratios of corresponding sides to see if they are equal.

20. Pre-Algebra 7-6 Similar Figures Try This: Example 3 Which rectangles are similar? A 8 ft 4 ft B6 ft 3 ft C 5 ft 2 ft Since the three figures are all rectangles, all the angles are right angles. So the corresponding angles are congruent.

21. Pre-Algebra 7-6 Similar Figures Try This: Example 3 16  20 The ratios are equal. Rectangle A is similar to rectangle B. The notation A ~ B shows similarity. The ratios are not equal. Rectangle A is not similar to rectangle C. 24 = 24 length of rectangle A length of rectangle B width of rectangle A width of rectangle B 8 6 4343 ? = length of rectangle A length of rectangle C width of rectangle A width of rectangle C 8 5 4242 ? = Compare the ratios of corresponding sides to see if they are equal.

22. Pre-Algebra 7-6 Similar Figures 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. 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. Which rectangles are similar? 17 in. 3.75 ft A and B are similar.