Scale Drawings and Proportions: Comparison and Dimension Finding

1. HW: Page 370 #1-6 and #21-26

2. Pre-Algebra Homework Page 374 #7-12 & #30-34 (Spiral Review)

3. Ch. 7 Learning Goal: Ratios & Proportions • Learn to find equivalent ratios to create proportions (7-1) • Learn to work with rates and ratios (7-2) • Learn to use one or more conversion factors to solve rate problems (7-3) • Learn to solve proportions (7-4) • Learn to identify and create dilations of plane figures (7-5) • Learn to determine whether figures are similar, to use scale factors, and to find missing dimensions similar figures (7-6) • Learn to make comparisons between and find dimensions of scale drawings and actual objects (7-7) • Learn to make comparisons between and find dimensions of scale models and actual objects (7-8) • Learn to make scale models of solid figures (7-9)

4. 7-7 Scale Drawings Warm Up Problem of the Day Lesson Presentation Pre-Algebra

5. 7-7 Scale Drawings 3 4 1 10 2 1 5 4 Pre-Algebra Warm Up Evaluate the following for x = 16. 1.3x2.x Evaluate the following for x = . 3. 10x4.x 48 12 4

6. Problem of the Day An isosceles triangle with a base length of 6 cm and side lengths of 5 cm is dilated by a scale factor of 3. What is the area of the image? 108 cm2

7. Today’s Learning Goal Assignment Learn to make comparisons between and find dimensions of scale drawings and actual objects.

8. Vocabulary scale drawing scale reduction enlargement

9. A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar to the object. A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

10. Reading Math The scale a:b is read “a to b.” For example, the scale 1 cm:3 ft is read “one centimeter to three feet.” 1 4 1 4

11. 2 cm Set up proportion using 8 m 1 cm x m scale length . actual length Additional Example 1A: Using Proportions to Find Unknown Scales or Lengths A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale? = 1  8 = x 2 Find the cross products. 8 = 2x 4 = x Solve the proportion. The scale is 1 cm:4 m.

12. 4 cm Set up proportion using 12 m 1 cm x m scale length . actual length Try This: Example 1A A. The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale? = 1  12 = x 4 Find the cross products. 12 = 4x 3 = x Solve the proportion. The scale is 1 cm:3 m.

13. 1.5 in. Set up proportion using x ft 1 in. 6 ft scale length . actual length Additional Example 1B: Using Proportions to Find Unknown Scales or Lengths B. The length of an object on a scale drawing is 1.5 inches. The scale is 1 in:6 ft. What is the actual length of the object? = 1 x = 6  1.5 Find the cross products. x = 9 Solve the proportion. The actual length is 9 ft.

14. 2 in. Set up proportion using x ft 1 in. 4 ft scale length . actual length Try This: Example 1B B. The length of an object on a scale drawing is 2 inches. The scale is 1 in:4 ft. What is the actual length of the object? = 1 x = 4  2 Find the cross products. x = 8 Solve the proportion. The actual length is 8 ft.

15. A scale drawing that is smaller than the actual object is called a reduction. A scale drawing can also be larger than the object. In this case, the drawing is referred to as an enlargement.

16. 8 mm = x mm 1000 1 scale length actual length Additional Example 2: Life Sciences Application Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? 1000 x = 1  8 Find the cross products. x = 0.008 Solve the proportion. The actual length of the amoeba is 0.008 mm.

17. 1 mm = x mm 10,000 1 scale length actual length Try This: Example 2 Under a 10,000:1 microscope view, a fiber appears to have length of 1mm. What is its actual length? 10,000 x = 1  1 Find the cross products. x = 0.0001 Solve the proportion. The actual length of the fiber is 0.0001 mm.

18. A drawing that uses the scale in. = 1 ft is said to be in in. scale. Similarly, a drawing that uses the scale in. = 1 ft is in in. scale. 1 4 1 4 1 2 1 2

19. A. If a wall in a in. scale drawing is 4 in. tall, how tall is the actual wall? 1 = 4 4 in. x ft. 0.25 in. 1 ft scale length actual length Additional Example 3A: Using Scales and Scale Drawings to Find Heights Length ratios are equal. Find the cross products. 0.25 x = 1  4 Solve the proportion. x = 16 The wall is 16 ft tall.

20. 1 = 2 4 in. x ft. 0.5 in. 1 ft scale length actual length Additional Example 3B: Using Scales and Scale Drawings to Find Heights B. How tall is the wall if a in. scale is used? Length ratios are equal. Find the cross products. 0.5 x = 1  4 Solve the proportion. x = 8 The wall is 8 ft tall.

21. A. If a wall in a in. scale drawing is 0.5 in. thick, how thick is the actual wall? 1 = 4 0.5 in. x ft. 0.25 in. 1 ft scale length actual length Try This: Example 3A Length ratios are equal. Find the cross products. 0.25 x = 1  0.5 Solve the proportion. x = 2 The wall is 2 ft thick.

22. 1 = 2 0.5 in. x ft. 0.5 in. 1 ft scale length actual length Try This: Example 3A Continued B. How thick is the wall if a in. scale is used? Length ratios are equal. Find the cross products. 0.5 x = 1  0.5 Solve the proportion. x = 1 The wall is 1 ft thick.

23. 1 4 Lesson Quiz 1. What is the scale of a drawing in which a 9 ft wall is 6 cm long? 2. Using a in. = 1 ft scale, how long would a drawing of a 22 ft car be? 3. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person? The scale of a map is 1 in. = 21 mi. Find each length on the map. 4. 147 mi 5. 5.25 mi 1 cm = 1.5 ft. 5.5 in. 72 in. 7 in. 0.25 in.