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8.1 Ratio and Proportion

8.1 Ratio and Proportion. Geometry--Honors Mrs. Blanco . Investigating Ratios. Put your name and each of your measurements into appropriate blank on the spreadsheet. Computing Ratios. If a and b are two quantities that are measured in the same units, then the ratio of a to b is a/b.

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8.1 Ratio and Proportion

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  1. 8.1 Ratio and Proportion Geometry--Honors Mrs. Blanco

  2. Investigating Ratios Put your name and each of your measurements into appropriate blank on the spreadsheet.

  3. Computing Ratios • If a and b are two quantities that are measured in the same units, then the ratio of ato bis a/b. • also written as a:b. • Because a ratio is a quotient, its denominator cannot be zero. • Ratios are usually expressed in simplified form. For instance, the ratio of 6:8 is usually simplified to 3:4.

  4. Ex. 1: Simplifying Ratios • Simplify the ratios: a. 12 cm b. 6 ft c. 9 in. 4 cm 18 in 18 in. Answers: a. b. c.

  5. The perimeter of rectangle ABCD is 60 centimeters. The ratio of BC: AB is 3:2. Find the length and the width of the rectangle Ex. 2: Using Ratios l=3x and w=2x

  6. 2l+ 2w = P 2(3x) + 2(2x) = 60 6x + 4x = 60 10x = 60 x = 6 Solution: So, ABCD has a length of 18 centimeters and a width of 12 cm.

  7. Slide #7

  8. The measures of the angles in ∆JKL are in the extended ratio 1:2:3. Find the measures of the angles. Ex. 3: Using Extended Ratios 2x° 3x° x°

  9. x°+ 2x°+ 3x° = 180° 6x = 180 x = 30 Solution: So, the angle measures are 30°, 2(30°) = 60°, and 3(30°) = 90°.

  10. The ratios of the side lengths of ∆DEF to the corresponding side lengths of ∆ABC are 2:1. Find the unknown lengths. Ex. 4: Using Proportions DF=6, FE=10, AB=4, CB=5

  11. An equation that equates two ratios is called a proportion. Using Proportions Means Extremes  =  The numbers a and d are the extremes of the proportions. The numbers b and c are the means of the proportion.

  12. Properties of proportions CROSS PRODUCT PROPERTY. The product of the extremes equals the product of the means. If  = , then ad = bc

  13. Ex. 5: Solving Proportions 3 2 4 5 = = y + 2 y x 7 3y = 2(y+2) 28 3y = 2y+4 x = 5 y 4 =

  14. The ratios of the side lengths of ∆DEF to the corresponding side lengths of ∆ABC are 5:3. Find the unknown lengths. Ex. 4: Using Proportions 10 cm 10 cm DF=16 2/3 cm AB=6 cm

  15. Properties of proportions RECIPROCAL PROPERTY. If two ratios are equal, then their reciprocals are also equal. If  = , then =  b a

  16. In the diagram Section 8.2 Ex. 2: Using Properties of Proportions AB AC = BD CE Find the length of BD.

  17. Solution AB = AC BD CE 16 = 20 x 10 20x = 160 x = 8 So, the length of BD is 8.

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