1 / 18

Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 9 27. 3 5. 6 x. x 75. 2.4 8. x 6. =. =. =. Warm Up Solve each proportion. 1. 2. x = 45. x = 20. x 3.5. 8 7. 3. 4. x = 4. =. x = 2. California Standards.

naida-good
Download Presentation

Warm Up

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. Preview Warm Up California Standards Lesson Presentation

  2. 927 3 5 6 x x 75 2.4 8 x 6 = = = Warm Up Solve each proportion. 1. 2. x = 45 x = 20 x 3.5 8 7 3. 4. x = 4 = x = 2

  3. California Standards Extension of MG1.2 Construct and read drawings and models made to scale.

  4. Vocabulary indirect measurement

  5. Sometimes, distances cannot be measured directly. One way to find such a distance is to use indirect measurement, a way of using similar figures and proportions to find a measure.

  6. F B 9 ft 3 ft A C 4 ft G E x Additional Example 1: Geography Application Triangles ABC and EFG are similar. Find the length of side EG. Triangles ABC and EFG are similar.

  7. 36 EF 9 EG x 3 AB 3x 3 4 3 AC Additional Example 1 Continued Triangles ABC and EFG are similar. Find the length of side EG. = Set up a proportion. Substitute 3 for AB, 4 for AC, and 9 for EF. = 3x = 36 Find the cross products. = Divide both sides by 3. x = 12 The length of side EG is 12 ft.

  8. H x E 7 in 8 in D F I G Check It Out! Example 1 Triangles DEF and GHI are similar. Find the length of side HI. 2 in Triangles DEF and GHI are similar.

  9. GH 56 8 2 HI x DE 2x 2 2 7 EF Check It Out! Example 1 Continued Triangles DEF and GHI are similar. Find the length of side HI. = Set up a proportion. Substitute 2 for DE, 7 for EF, and 8 for GH. = 2x = 56 Find the cross products. = Divide both sides by 2. x = 28 The length of side HI is 28 in.

  10. 1 Understand the Problem Additional Example 2: Problem Solving Application A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a shadow that is 35 ft long. How tall is the tree? The answer is the height of the tree. List theimportant information: • The length of the building’s shadow is 75 ft. • The height of the building is 30 ft. • The length of the tree’s shadow is 35 ft.

  11. 3 Solve Make a Plan h 30 feet 35 feet 75 feet 2 Additional Example 2 Continued Use the information to draw a diagram. Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

  12. 3 Solve 1050 75 75h 75 Additional Example 2 Continued 30 75 h 35 Corresponding sides of similar figures are proportional. = 75h = 1050 Find the cross products. = Divide both sides by 75. h = 14 The height of the tree is 14 feet.

  13. 4 Additional Example 2 Continued Look Back 75 30 Since = 2.5, the building’s shadow is 2.5 times its height. So, the tree’s shadow should also be 2.5 times its height and 2.5 of 14 is 35 feet.

  14. 1 Understand the Problem Check It Out! Example 2 A 24-ft building casts a shadow that is 8 ft long. A nearby tree casts a shadow that is 3 ft long. How tall is the tree? The answer is the height of the tree. List theimportant information: • The length of the building’s shadow is 8 ft. • The height of the building is 24 ft. • The length of the tree’s shadow is 3 ft.

  15. 3 Solve Make a Plan h 24 feet 3 feet 8 feet 2 Check It Out! Example 2 Continued Use the information to draw a diagram. Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

  16. 3 Solve 8h 8 72 8 Check It Out! Example 2 Continued 24 8 h 3 Corresponding sides of similar figures are proportional. = 72 = 8h Find the cross products. = Divide both sides by 8. 9 = h The height of the tree is 9 feet.

  17. 4 Check It Out! Example 2 Continued Look Back 8 24 1 3 Since = , the building’s shadow is times its height. So, the tree’s shadow should also be times its height and of 9 is 3 feet. 1 3 1 3 1 3

  18. w 5 m 7 m 5.7 m Lesson Quiz 1. Vilma wants to know how wide the river near her house is. She drew a diagram and labeled it with her measurements. How wide is the river? 2. A yardstick casts a 2 ft shadow. At the same time, a tree casts a shadow that is 6 ft long. How tall is the tree? 7.98 m 9 ft

More Related