1. 4-6 Scale Drawings and Scale Models Lesson 4.6

2. 4-6 Scale Drawings and Scale Models Warm Up Write the two requirements needed for two figures to be SIMILAR: 1. 2. Corresponding angles are equal Corresponding sides form equivalent ratios.

3. 4-6 Scale Drawings and Scale Models Today’s Goal: Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.

4. 4-6 Scale Drawings and Scale Models Vocabulary scale drawing scale factor scale model scale

5. 4-6 Scale Drawings and Scale Models A scale drawing is a proportional two-dimensional drawing of an object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor.

6. 4-6 Scale Drawings and Scale Models A scale is the ratio between two sets of measurements. Scales can use the same units or different units. A scale model is a proportional three- dimensional model of an object.

7. 4-6 Scale Drawings and Scale Models Identify the scale factor. Example 1 13.5108Width (in.)‏ 18144Length (in.)‏ BlueprintRoom blueprint length room length = 1818 1818 The scale factor is. Write a ratio using one of the dimensions. Simplify. 18 144 = A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions. Caution!

8. 4-6 Scale Drawings and Scale Models Example 2 Identify the scale factor. 312Length (in.)‏ Toy CarCar The scale factor is. 1414

9. 4-6 Scale Drawings and Scale Models On a scale drawing, a bookshelf is 8 inches tall. The scale factor is. What is the height of the bookshelf? Example 3 1818 Think: drawing bookshelf = 1818 8h8h = 1818 h = 64 Write a proportion to find the length l. Find the cross products.

10. 4-6 Scale Drawings and Scale Models On a scale drawing, with a scale of 1 cm: 3m, the height of a tree is 5.2 cm. How tall is the actual tree? Example 4 Think: drawing tree = 1313 5.2 h = 1313 h = 15.6 m Write a proportion to find the length h. Find the cross products.

11. 4-6 Scale Drawings and Scale Models Check It Out: Example 3 On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers? Let d be the actual distance between the cities. 1 50 = 7d7d 1 · d = 50 · 7 1d = 350 d = 350 The distance between the cities is 350 kilometers. Write a proportion. Find the cross products. Multiply.

12. 4-6 Scale Drawings and Scale Models

13. 4-6 Scale Drawings and Scale Models On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles? Additional Example 3: Measurement Application Let d be the actual distance between the cities. 1.5 60 = 7.5 d 1.5 · d = 60 · 7.5 1.5d = 450 1.5d 1.5 = 450 1.5 d = 300 The distance between the cities is 300 miles. Write a proportion. Find the cross products. Multiply. Divide both sides by 1.5.

14. 4-6 Scale Drawings and Scale Models Check It Out: Example 1 Identify the scale factor. 318Wing span (in.)‏ 212Length (in.)‏ BlueprintModel Aircraft blueprint length aircraft length = 2 12 = 1616 Write a ratio using one of the dimensions. Simplify. The scale factor is. 1616

15. 4-6 Scale Drawings and Scale Models A scale is the ratio between two sets of measurements. Scales can use the same units or different units. A scale model is a proportional three- dimensional model of an object.

16. 4-6 Scale Drawings and Scale Models A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is. Find the size of the photograph. Additional Example 2: Using Scale Factors to Find Unknown Lengths 5151 Think: poster photo = 5151 36 l = 5151 5l = 36 l = 7.2 Write a proportion to find the length l. Find the cross products. Divide.

17. 4-6 Scale Drawings and Scale Models A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is. Find the size of the photograph. Additional Example 2 Continued 5151 Think: poster photo = 5151 20.5 w = 5151 5w = 20.5 w = 4.1 Write a proportion to find the width w. Find the cross products. Divide. The photo is 7.2 in. long and 4.1 in. wide.