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

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

3. 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

4. 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 to solve for all the missing sides

5. 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

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

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

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

9. 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 , which reduces to 3 4

10. 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

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

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