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Understanding Ratios and Proportions in Geometry

Learn about ratios, proportion, cross products, and how to use ratios in geometry problems. Explore examples and applications to deepen your understanding of this fundamental concept in mathematics.

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Understanding Ratios and Proportions in Geometry

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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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