1. Using Proportions with Similar Polygons
January 2013

2. Polygons
A polygon is a closed figure formed by three or more connected line segments
Congruent polygons have the same exact dimensions
Same angle measures
Same lengths for all sides
Similar polygons have the same angle measures but the sides are not the same length
The sides are in proportion

3. These polygons are congruent
These polygons are congruent. They have the same shape and the same size.

4. These figures are similar
These figures are similar. They have the same shape, their angles are equal and their sides are proportional.

5. Since similar figures are proportional, we can use proportions to solve for missing measures.

6. You must match the corresponding sides.
A D
BE
CF B A E D F C

7. Be careful!!! Sometimes the figures may have a different orientation (they may be turned a different way).

8. Matching corresponding sides just means you are going to match the long side of one figure with the long side on the other figure, and so on.
A B C D E F

9. Match the corresponding sides on the figures below.
Large Small
Side A ___
Side B ___
Side C ___ F D E
A B C D E F

10. Use proportions to solve for side B.
Large Small
Short ___ ___
Long 5 4 B
6.88
7 B 5
6.88 4 F

11. Cross Multiply and Solve for B

12. Use proportions to solve for side F.
Large Small
Medium ___ ___
Short 7 F 5 4
7 8.6 5
6.88 4 F

13. Cross Multiply and Solve for F

14. Practice ABCD ~ EFGH Solve for x. 4x = 12 x = 3 B A E F 4 2 G D H C x6
4x = 12
x = 3

15. Practice Determine whether the following shapes are similar
That means, we have to determine if the sides are in proportion! 3 4 16 12
3*28 = 7*12
84 = 84  Yes! 7 28

16. Homework
In your textbook Pg. 388 #1-14