1 / 18

8.2 Problem Solving in Geometry with Proportions

8.2 Problem Solving in Geometry with Proportions. Geometry Mr. Davenport. Use properties of proportions Use proportions to solve real-life problems such as using the scale of a map. Reminder: Test after 8.3. Objectives. Using the properties of proportions.

charlene-durham
Download Presentation

8.2 Problem Solving in Geometry with Proportions

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. 8.2 Problem Solving in Geometry with Proportions Geometry Mr. Davenport

  2. Use properties of proportions Use proportions to solve real-life problems such as using the scale of a map. Reminder: Test after 8.3. Objectives Slide #2

  3. Using the properties of proportions • In Lesson 8.1, you studied the reciprocal property and the cross product property. Two more properties of proportions, which are especially useful in geometry, are given on the next slides. • You can use the cross product property and the reciprocal property to help prove these properties. Slide #3

  4. Additional Properties of Proportions IF a b a c , then = = c d b d IF a c a + b c + d , then = = b d b d Slide #4

  5. Ex. 1: Using Properties of Proportions IF p 3 p r , then = = r 5 6 10 p r Given = 6 10 p 6 a c a b = = = , then b d c d r 10 Slide #5

  6. Ex. 1: Using Properties of Proportions IF p 3 = Simplify r 5  The statement is true. Slide #6

  7. Ex. 1: Using Properties of Proportions a c Given = 3 4 a + 3 c + 4 a c a + b c + d = = = , then 3 4 b d b d Because these conclusions are equivalent, the statement is true. a + 3 c + 4 = 3 4 Slide #7

  8. In the diagram Ex. 2: Using Properties of Proportions AB AC = BD CE Find the length of BD. Do you get the fact that AB ≈ AC? Slide #8

  9. Solution AB = AC BD CE 16 = 30 – 10 x 10 16 = 20 x 10 20x = 160 x = 8 Given Substitute Simplify Cross Product Property Divide each side by 20. So, the length of BD is 8. Slide #9

  10. Geometric Mean • The geometric mean of two positive numbers a and b is the positive number x such that a x If you solve this proportion for x, you find that x = √a ∙ b which is a positive number. = x b Slide #10

  11. Geometric Mean Example • For example, the geometric mean of 8 and 18 is 12, because 8 12 = 12 18 and also because x = √8 ∙ 18 = x = √144 = 12 Slide #11

  12. PAPER SIZES. International standard paper sizes are commonly used all over the world. The various sizes all have the same width-to-length ratios. Two sizes of paper are shown, called A4 and A3. The distance labeled x is the geometric mean of 210 mm and 420 mm. Find the value of x. Ex. 3: Using a geometric mean Slide #12

  13. Solution: The geometric mean of 210 and 420 is 210√2, or about 297mm. 210 x Write proportion = x 420 X2 = 210 ∙ 420 X = √210 ∙ 420 X = √210 ∙ 210 ∙ 2 X = 210√2 Cross product property Simplify Factor Simplify Slide #13

  14. Using proportions in real life • In general when solving word problems that involve proportions, there is more than one correct way to set up the proportion. Slide #14

  15. Ex. 4: Solving a proportion • MODEL BUILDING. A scale model of the Titanic is 107.5 inches long and 11.25 inches wide. The Titanic itself was 882.75 feet long. How wide was it? Width of Titanic Length of Titanic = Width of model Length of model LABELS: Width of Titanic = x Width of model ship = 11.25 in Length of Titanic = 882.75 feet Length of model ship = 107.5 in. Slide #15

  16. Write the proportion. Substitute. Multiply each side by 11.25. Use a calculator. Reasoning: Width of Titanic Length of Titanic = Width of model Length of model x feet 882.75 feet = 11.25 in. 107.5 in. 11.25(882.75) x = 107.5 in. x ≈ 92.4 feet So, the Titanic was about 92.4 feet wide. Slide #16

  17. Note: • Notice that the proportion in Example 4 contains measurements that are not in the same units. When writing a proportion in unlike units, the numerators should have the same units and the denominators should have the same units. • The inches (units) cross out when you cross multiply. Slide #17

  18. Assignment • Section 8.2  P. 468 / 10-34 even Slide #18

More Related