# Chapter9 - Proportions and Similarity Proportions and...

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Unformatted text preview: Proportions and Similarity Proportions and Similarity Â§ 9.1 Using Ratios and Proportions 9.1 Using Ratios and Proportions Â§ 9.4 Proportional Parts and Triangles 9.4 Proportional Parts and Triangles Â§ 9.3 Similar Triangles 9.3 Similar Triangles Â§ 9.2 Similar Polygons 9.2 Similar Polygons Â§ 9.6 Proportional Parts and Parallel Lines 9.6 Proportional Parts and Parallel Lines Â§ 9.5 Triangles and Parallel Lines 9.5 Triangles and Parallel Lines Â§ 9.7 Perimeters and Similarity 9.7 Perimeters and Similarity Using Ratios and Proportions Using Ratios and Proportions You will learn to use ratios and proportions to solve problems. 1) ratio 2) proportion 3) cross products 4) extremes 5) means Using Ratios and Proportions Using Ratios and Proportions In 2000, about 180 million tons of solid waste was created in the United States. The paper made up about 72 million tons of this waste. The ratio of paper waste to total waste is 72 to 180. This ratio can be written in the following ways. 72 to 180 72:180 72 Ã· 180 180 72 Definition of Ratio A ratio is a comparison of two numbers by division. a to b a:b a Ã· b b a where b Using Ratios and Proportions Using Ratios and Proportions A __________ is an equation that shows two equivalent ratios. proportion 3 2 30 20 = Every proportion has two cross products . In the proportion to the right, the terms 20 and 3 are called the extremes , and the terms 30 and 2 are called the means . The cross products are 20(3) and 30(2). The cross products are always _____ in a proportion. equal 30(2) = 20(3) 60 = 60 Using Ratios and Proportions Using Ratios and Proportions Theorem 9-1 Property of Proportions For any numbers a and c and any nonzero numbers b and d , , if d c b a = Likewise, , if bc ad = then , if 2 1 10 5 = ( 29 ( 29 ( 29 ( 29 1 10 2 5 = 2 1 10 5 = ( 29 ( 29 ( 29 ( 29 then If 1 10 2 5 = bc ad = then . then d c b a = Using Ratios and Proportions Using Ratios and Proportions Solve each proportion: 30 15 2 6 = x 15(2x) = 30(6) 30x = 180 x = 6 2 3 30 =- x x 3(x) = (30 â€“ x)2 3x = 60 â€“ 2x 5x = 60 x = 12 Using Ratios and Proportions Using Ratios and Proportions The gear ratio is the number of teeth on the driving gear to the number of teeth on the driven gear. Driving gear Driven gear If the gear ratio is 5:2 and the driving gear has 35 teeth, how many teeth does the driven gear have? given ratio equivalent ratio = 5 2 35 x = driving g e a r drive n g e a r driving g e a r drive n g e a r 5 x = 70 x = 14 The driven gear has 14 teeth. Using Ratios and Proportions Using Ratios and Proportions Similar Polygons Similar Polygons Yo u will le a rn to ide ntify s im ila r po lyg o ns . 1) po lyg o ns 2) s ide s 3) s im ila r po lyg o ns 4) s c a le dra wing Similar Polygons Similar Polygons A polygon is a ______ figure in a plane formed by segments called sides . c lo s e d It is a general term used to describe a geometric figure with at least three sides.It is a general term used to describe a geometric figure with at least three sides....
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Chapter9 - Proportions and Similarity Proportions and...

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