Using Proportions To Solve For Missing Sides Similar Figures Using Proportions To Solve For Missing Sides

Definition of Similar Figures To Shapes are similar if: Every Corresponding Angle is Congruent Every Corresponding Side is Proportional

Example 1 ABCD ~ WXYZ W A m 6 B X 7 21 n D 15 9 C Z p Y If you are given 2 shapes are similar then you can use proportions to Find missing values

Example 1 ABCD ~ WXYZ W A m 6 B X 7 21 n D 15 9 C Z p Y Since 7 and 21 are corresponding sides and we know each value, we can use the ratio 7 21 to solve for all the missing sides

Example 1 Use the sides that correspond to each other to set up equal proportions ABCD ~ WXYZ W A m 6 B X 7 21 n D 15 9 C Z p Y 7 21 = 6 𝑚 7 21 = 𝑛 15 7 21 = 9 𝑝

Now solve each proportion Example 1 Now solve each proportion 7 21 = 6 𝑚 7m = 126 Cross Multiply m = 18 Division Property

Now solve each proportion Example 1 Now solve each proportion 7 21 = 𝑛 15 7n = 105 Cross Multiply n = 15 Division Property

Now solve each proportion Example 1 Now solve each proportion 7 21 = 9 𝑝 7p = 189 Cross Multiply p = 27 Division Property

Example 2 Begin by using the ratio 12 16 , which reduces to 3 4 Often the Ratios do not Simplify nicely… In this case either leave answer as a fraction or make it a decimal H E EFG ~ HIJ 9 x y 6 J G 12 16 F I Begin by using the ratio 12 16 , which reduces to 3 4

Use the corresponding sides to set up the proportions Example 2 Use the corresponding sides to set up the proportions H E EFG ~ HIJ 9 x y 6 J G 12 16 F I 3 4 = 6 𝑦 3 4 = 𝑥 9

Now solve each proportion Example 2 Now solve each proportion 3 4 = 𝑥 9 4x = 27 Cross Multiply x = 27 4 = 6.75 Division Property

Now solve each proportion Example 2 Now solve each proportion 3 4 = 6 𝑦 3y = 24 Cross Multiply y = 8 Division Property