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7-1 Vocabulary

7-1 Vocabulary. Ratio Proportion Extremes Means Cross products. 7-1 Ratio and Proportion. Geometry. 7-1 Ratio. A ratio is a comparison of two numbers with the same units by division. The ratio of 2 to 5 can be expressed three different ways; 2 to 5 2:5 2/5.

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7-1 Vocabulary

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  1. 7-1 Vocabulary • Ratio • Proportion • Extremes • Means • Cross products

  2. 7-1 Ratio and Proportion Geometry

  3. 7-1 Ratio • A ratio is a comparison of two numbers with the same units by division. • The ratio of 2 to 5 can be expressed three different ways; 2 to 5 2:5 2/5

  4. Slope is a ratio, too • Slope formula

  5. Ex. 1 Write a ratio expressing the slope of AB. • A(-1,3), B(2, -2)

  6. Ratios • A ratio can involve more than 2 numbers. • Ex. 2) The ratio of the side lengths of a triangle is 4:7:5 and its perimeter is 96 cm. What is the length of the shortest side?

  7. Cross Product Property of Proportions • In a proportion, the product of the extremes(ad) is equal to the product of the means(bc). • If , then ad = bc.

  8. Ex. 3 Solve each proportion.

  9. Ratio’s (cont’d) • Basically, a ratio has to be a comparison of only like labels (in., ft., yd., & mile) • Referring to our previous example, then 2 ft to 5 ft we can write as a ratio, 2:5. • If we had 3 ft. to 7 in., then we would have to change feet to inches first. 3 • 12 = ___ __ in. to 7 in. OR ___/7

  10. Converting Ratios • Ratios with different units, convert to same units first. Then simplify the fraction just like you would normally. • Example 1 • a) b)

  11. Ex. 2 Find slope

  12. Using Ratios • Example 2 -The perimeter of the isosceles triangle shown is 56 in. The ratio of LM:MN is 5:4. Find the lengths of the sides and the base of the triangle.

  13. Using extended ratios • Example 3 – The measures of the sides in a triangle are in the extended ratio 4:7:5 & its perimeter is 96 cm. What is the length of the shortest side?

  14. Application Ex. 4) Marla is making a scale drawing of her bedroom. Her rectangular room is 12 ½ feet wide and 15 feet long. On the scale drawing, the width of the room is 5 inches. What is the length?

  15. Assignment

  16. Ex. 4 • The ratio of the measures of angles is 5:12:19. What is the measure of the largest angle?

  17. Example 1- Solving Proportions a) b)

  18. Example 2

  19. Example 3

  20. Example 4 • A photo of a building has the measurements given in the sketch below. The actual building is 26¼ ft wide. How tall is it? • What is the height of the door in the actual building?

  21. Reciprocal Property • If two ratios are equal, then their reciprocals are also equal. • If then

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