7-1 Ratio and Proportion Warm Up Lesson Presentation Lesson Quiz Holt Geometry

Do Now 1. Solve each equation. 2. 4x + 5x + 6x = 45 3. (x – 5)2 = 81 4. Write in simplest form.

Objectives Write and simplify ratios. Use proportions to solve problems.

Vocabulary ratio proportion extremes means cross products scale

A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b, a:b, or , where b ≠ 0. For example, the ratios 1 to 2, 1:2, and all represent the same comparison.

In a ratio, the denominator of the fraction cannot be zero because division by zero is undefined. Remember!

Example 1: Writing Ratios Write a ratio expressing the slope of l.

Example 2 Given that two points on m are C(–2, 3) and D(6, 5), write a ratio expressing the slope of m.

A ratio can involve more than two numbers A ratio can involve more than two numbers. For the rectangle, the ratio of the side lengths may be written as 3:7:3:7.

Example 3: Using Ratios 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?

Example 4 The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle?

A proportion is an equation stating that two ratios are equal. In the proportion , the values a and d are the extremes. The values b and c are the means. When the proportion is written as a:b = c:d, the extremes are in the first and last positions. The means are in the two middle positions.

In Algebra 1 you learned the Cross Products Property In Algebra 1 you learned the Cross Products Property. The product of the extremes ad and the product of the means bc are called the cross products.

The Cross Products Property can also be stated as, “In a proportion, the product of the extremes is equal to the product of the means.” Reading Math

Example 5: Solving Proportions Solve the proportion.

Example 5a Solve the proportion.

The following table shows equivalent forms of the Cross Products Property.

Example 6: Using Properties of Proportions Given that 18c = 24d, find the ratio of d to c in simplest form.

Example 7 Given that 16s = 20t, find the ratio t:s in simplest form.

A scale drawing represents an object as smaller than or larger than its actual size. The drawing’s scale is the ratio of any length in the drawing to the corresponding actual length. For example, on a map with a scale of 1 cm : 1500 m, one centimeter on the map represents 1500 m in actual distance.

Example 8 The rectangular central chamber of the Lincoln Memorial is 74 ft long and 60 ft wide. Make a scale drawing of the floor of the chamber using a scale of 1 in.:20 ft.

Example 9: Making a Scale Drawing Lady Liberty holds a tablet in her left hand. The tablet is 7.19 m long and 4.14 m wide. If you made a scale drawing using the scale 1 cm:0.75 m, what would be the dimensions to the nearest tenth?

Exit Slip 1. The ratio of the angle measures in a triangle is 1:5:6. What is the measure of each angle? Solve each proportion. 2. 3. 4. Given that 14a = 35b, find the ratio of a to b in simplest form. 5. An apartment building is 90 ft tall and 55 ft wide. If a scale model of this building is 11 in. wide, how tall is the scale model of the building? 15°, 75°, 90° 3 9 18 in.

Exit Slip 1. The ratio of the angle measures in a triangle is 1:5:6. What is the measure of each angle? Solve each proportion. 2. 3. 4. Given that 14a = 35b, find the ratio of a to b in simplest form. 5. An apartment building is 90 ft tall and 55 ft wide. If a scale model of this building is 11 in. wide, how tall is the scale model of the building?

Exit Slip 1. The ratio of the angle measures in a triangle is 1:5:6. What is the measure of each angle? Solve each proportion. 2. 3. 4. Given that 14a = 35b, find the ratio of a to b in simplest form. 5. An apartment building is 90 ft tall and 55 ft wide. If a scale model of this building is 11 in. wide, how tall is the scale model of the building?