1. Section 4-2: Proportions and Similar Figures SPI 12F: Select ratios and proportions to represent real-world problems Objective: use proportions to find measures of similar figures. Proportion: an equation that states that two ratios are equal. a = c or a:b = c:d b d

2. Proportions in Review Find the Unit Rate A 10 ounce bottle of shampoo costs $2.40. What is the cost per ounce? 2.40 = $.24 10 The cost per ounce is $.24 Conversion Factor A sloth travels 0.15 miles per hour. Convert this speed to feet per minute. (5280 ft = 1 mi.) 0.15 mi 5280 ft 1 hr = 13.2 ft/min 1 hr 1 mi 60 min Solve Proportion Solve the following proportions. a = 90m = 3

3. Proportions and Similar Figures ∆ ABC ~ ∆ FGH (similar): This means corresponding angles are congruent corresponding sides are proportional the order of the letters indicate corresponding angles

4. Proportions and Similar Figures ∆ ABC ~ ∆ DFE: Find the length of DE. Define x as DE: Substitute in known values. Solve proportion.

5. Apply Similarity (Real-world) A tree casts a shadow 7.5 feet long. A woman 5 ft tall casts a shadow 3 ft long. The triangle show for the tree and its shadow is similar to the triangle shown for the woman and her shadow. How tall is the tree? Write a proportion statement and solve. Label the diagram with known information and a variable to show the unknown x 5

6. Scale Drawing The scale of the map is 1 inch : 10 miles. Approximately how far is it from Valkaria to Wabasso? Write a proportion statement and solve.