1 / 22

Chapter 7

Chapter 7 . 7-5 Using proportional relationships. Objectives. Use ratios to make indirect measurements. Use scale drawings to solve problems. Indirect measurement.

ordell
Download Presentation

Chapter 7

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. Chapter 7 7-5 Using proportional relationships

  2. Objectives Use ratios to make indirect measurements. Use scale drawings to solve problems.

  3. Indirect measurement • Indirect measurementis any method that uses formulas, similar figures, and/or proportions to measure an object. The following example shows one indirect measurement technique.

  4. Helpful Hint Whenever dimensions are given in both feet and inches, you must convert them to either feet or inches before doing any calculations. Hint

  5. Example 1: Measurement Application • Tyler wants to find the height of a telephone pole. He measured the pole’s shadow and his own shadow and then made a diagram. What is the height h of the pole?

  6. solution • Step 1 Convert the measurements to inches. • AB = 7 ft 8 in. = (7  12) in. + 8 in. = 92 in. • BC = 5 ft 9 in. = (5  12) in. + 9 in. = 69 in. • FG = 38 ft 4 in. = (38  12) in. + 4 in. = 460 in. • Step 2 Find similar triangles. • Because the sun’s rays are parallel, A  F. Therefore ∆ABC ~ ∆FGH by AA ~.

  7. Step 3 Find h. Corr. sides are proportional. 92h = 69  460 h = 345 The height h of the pole is 345 inches, or 28 feet 9 inches.

  8. Check it out ! • A student who is 5 ft 6 in. tall measured shadows to find the height LM of a flagpole. What is LM? The height of the flagpole is 187 in., or 15 ft. 7 in.

  9. Scale drawing • A scale drawingrepresents an object as smaller than or larger than its actual size. The drawing’s scaleis the ratio of any length in the drawing • to the corresponding actual length. For example, on a map with a scale of 1 cm : 1500 m, one centimeter on the map represents 1500 m in actual distance

  10. Example 2: Solving for a Dimension • On a Wisconsin road map, Kristin measured a distance of 111/8 in. from Madison to Wausau. The scale of this map is 1inch:13 miles. What is the actual distance between Madison and Wausau to the nearest mile?

  11. solution • To find the actual distance x write a proportion comparing the map distance to the actual distance. x 145 The actual distance is 145 miles, to the nearest mile.

  12. Check it out!!! • Find the actual distance between City Hall and El Centro College. The actual distance is 900 meters, or 0.9 km.

  13. Example 3: Making a Scale Drawing • Lady Liberty holds a tablet in her left hand. The tablet is 7.19 m long and 4.14 m wide. If you made a scale drawing using the scale 1 cm:0.75 m, what would be the dimensions to the nearest tenth?

  14. Solution • Set up proportions to find the length l and width w of the scale drawing. 0.75w = 4.14 w  5.5 cm

  15. 3.7 in. 3 in. Check it out!!! • The rectangular central chamber of the Lincoln Memorial is 74 ft long and 60 ft wide. Make a scale drawing of the floor of the chamber using a scale of 1 in.:20 ft.

  16. Similar triangles

  17. Example 4: Using Ratios to Find Perimeters and Areas • Given that ∆LMN:∆QRT, find the perimeter P and area A of ∆QRS.

  18. Solution • Perimeter Area 13P = 36(9.1) 132A = (9.1)2(60) P = 25.2 A = 29.4 cm2 The perimeter of ∆QRS is 25.2 cm, and the area is 29.4 cm2.

  19. Check it out!!! • ∆ABC ~ ∆DEF, BC = 4 mm, and EF = 12 mm. If P = 42 mm and A = 96 mm2 for ∆DEF, find the perimeter and area of ∆ABC. • The perimeter of ∆ABC is 14 mm, and the area is 10.7 mm2.

  20. Student guided Practice • Do problems 2,3,5,7,10 and 11 in your book page 505

  21. Homework • Do problems 13-19 in your book page 505

More Related