1 / 19

8.1 Ratio and Proportion

8.1 Ratio and Proportion. Geometry Mrs. Spitz Spring 2005. Find and simplify the ratio of two numbers. Use proportions to solve real-life problems, such as computing the width of a painting. Chapter 8 Definitions Ch.8 Postulates/ Theorems WS 8.1A Due end of class WS 8.1B Homework

zohar
Download Presentation

8.1 Ratio and Proportion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 8.1 Ratio and Proportion Geometry Mrs. Spitz Spring 2005 Slide #1

  2. Find and simplify the ratio of two numbers. Use proportions to solve real-life problems, such as computing the width of a painting. Chapter 8 Definitions Ch.8 Postulates/ Theorems WS 8.1A Due end of class WS 8.1B Homework Quizzes after 8.3 and 8.5 and 8.7 Objectives/Assignment Slide #2

  3. Computing Ratios • If a and b are two quantities that are measured in the same units, then the ratio of a to be is a/b. The ratio of a to be can also be 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. (You divided by 2) Slide #3

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

  5. Ex. 1: Simplifying Ratios • Simplify the ratios: • 12 cm b. 6 ft 4 m 18 in Solution: To simplify the ratios with unlike units, convert to like units so that the units divide out. Then simplify the fraction, if possible. Slide #5

  6. Ex. 1: Simplifying Ratios • Simplify the ratios: • 12 cm 4 m 12 cm12 cm123 4 m 4∙100cm 400 100 Slide #6

  7. Ex. 1: Simplifying Ratios • Simplify the ratios: b. 6 ft 18 in 6 ft6∙12 in 72 in. 4 4 18 in 18 in. 18 in. 1 Slide #7

  8. The perimeter of rectangle ABCD is 60 centimeters. The ratio of AB: BC is 3:2. Find the length and the width of the rectangle Ex. 2: Using Ratios Slide #8

  9. SOLUTION: Because the ratio of AB:BC is 3:2, you can represent the length of AB as 3x and the width of BC as 2x. Ex. 2: Using Ratios Slide #9

  10. Statement 2l + 2w = P 2(3x) + 2(2x) = 60 6x + 4x = 60 10x = 60 x = 6 Reason Formula for perimeter of a rectangle Substitute l, w and P Multiply Combine like terms Divide each side by 10 Solution: So, ABCD has a length of 18 centimeters and a width of 12 cm. Slide #10

  11. The measures of the angles in ∆JKL are in the extended ratio 1:2:3. Find the measures of the angles. Begin by sketching a triangle. Then use the extended ratio of 1:2:3 to label the measures of the angles as x°, 2x°, and 3x°. Ex. 3: Using Extended Ratios 2x° 3x° x° Slide #11

  12. Statement x°+ 2x°+ 3x° = 180° 6x = 180 x = 30 Reason Triangle Sum Theorem Combine like terms Divide each side by 6 Solution: So, the angle measures are 30°, 2(30°) = 60°, and 3(30°) = 90°. Slide #12

  13. 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 Ratios Slide #13

  14. SOLUTION: DE is twice AB and DE = 8, so AB = ½(8) = 4 Use the Pythagorean Theorem to determine what side BC is. DF is twice AC and AC = 3, so DF = 2(3) = 6 EF is twice BC and BC = 5, so EF = 2(5) or 10 Ex. 4: Using Ratios 4 in a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 5 = c Slide #14

  15. An equation that equates two ratios is called a proportion. For instance, if the ratio of a/b is equal to the ratio c/d; then the following proportion can be written: 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. Slide #15

  16. Properties of proportions • CROSS PRODUCT PROPERTY. The product of the extremes equals the product of the means. If  = , then ad = bc Slide #16

  17. Properties of proportions • RECIPROCAL PROPERTY. If two ratios are equal, then their reciprocals are also equal. If  = , then =  b a To solve the proportion, you find the value of the variable. Slide #17

  18. Ex. 5: Solving Proportions 4 5 Write the original proportion. Reciprocal prop. Multiply each side by 4 Simplify. = x 7 4 x 7 4 = 4 5 28 x = 5 Slide #18

  19. Ex. 5: Solving Proportions 3 2 Write the original proportion. Cross Product prop. Distributive Property Subtract 2y from each side. = y + 2 y 3y = 2(y+2) 3y = 2y+4 y 4 = Slide #19

More Related