8.3 Similar Polygons How to identify similar polygons. How to use similar polygons to solve problems.

8.3 Similar Polygons Identifying Similar Polygons: Informally, one polygon is similar to another polygon if it has the same shape, but not necessarily the same size. Below are two examples. Similar parallelogramsSimilar hexagons Definition of Similar Polygons Two Polygons are similar if their corresponding angles are congruent and the lengths of corresponding sides are proportional. The symbol ~ is read “is similar to.” But more precisely:

8.3 Similar Polygons Is triangle similar to ? D E F A BC Show that the lengths of corresponding sides of each triangle are proportional. Have we shown that the lengths of corresponding sides proportional? Yes! And the common ratio of or 1:2 is called the scale factor of to. Yes, because their corresponding angles are congruent too!

8.3 Similar Polygons The two triangles below are similar. With your partner, solve for X on a half piece of paper. Show your work. D E F A BC 5 7 X 9

8.3 Similar Polygons Theorem 8.1 If two polygons are similar, then the ratio of their perimeters is equal to the ratio of their corresponding sides. E F A BC D Ratios of corresponding sides What about the ratio of their perimeters? They Are Equal!

8.3 Similar Polygons AA E D C B E D C B Figure 1Figure The figures below are similar. Determine the perimeter of figure 2. Theorem 8.1 If two polygons are similar, then the ratio of their perimeters is equal to the ratio of their corresponding sides. Remember -

8.3 Similar Polygons You work in a picture framing shop after school three days a week. One day after a particularly intriguing lesson in geometry, you are at work and your next job is to put a 8” x 10” picture in a frame with the outer dimensions of 10” x 12”. You now wonder with your new found knowledge – Are the separate rectangles formed by the picture and the outer edge of the frame similar polygons? 8” 10” 12” 10” They Are Not Equal !

8.3 Similar Polygons

Homework: Pg. 390 Problems