Using Proportions with Similar Polygons January 2013

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

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

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

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

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

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

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

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

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

Cross Multiply and Solve for B

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

Cross Multiply and Solve for F

Practice ABCD ~ EFGH Solve for x. 4x = 12 x = 3 B A E F 4 2 G D H C x 6 4x = 12 x = 3

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

Homework In your textbook Pg. 388 #1-14