Ratios, Rates and Percents Lesson 24 Ratios, Rates and Percents Ratios and Similar Figures

Warm-Up Sketch two congruent rectangles. Sketch two similar, but not congruent, triangles. Find the perimeter of the shape below.

Ratios and Similar Figures Target: Find missing sides or perimeters of figures using ratios.

Example 1 Two similar figures are shown below. Find the ratio of the smaller figure’s perimeter to the larger figure’s perimeter. Find ratio of sides. The ratio of the perimeters is or 1:2.

Example 2 Given the similar figures, use ratios to find the missing perimeter. Find ratio of corresponding sides. Find ratio of perimeters. Ratio of perimeters equals ratio of corresponding sides. Use equivalent fractions to find the larger perimeter. The perimeter of the triangle is 36 inches.

Example 3 Given the similar figures and perimeters, use ratios to find the length of the missing side. Find ratio of perimeters. Find ratio of corresponding sides. Ratio of perimeters equals ratios of corresponding sides. Use equivalent fractions to find the missing side. The missing side is 10 feet.

Exit Problems Find the ratio of the perimeters in the pair of similar figures given. The circumferences for a pair of similar circles are shown. Find the ratio of the corresponding diameters. The ratio of corresponding sides of two similar triangles is 2 : 3. The larger triangle has a perimeter of 12 cm. Find the perimeter of the smaller triangle.

Communication Prompt When two shapes are similar, why is the ratio of their corresponding sides equal to the ratio of their perimeters? Use an example to help you explain.