1. Similar Polygons

2. What are similar polygons?
Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.

3. Congruent Figures
In order to be congruent, two figures must be the same size and same shape.
~ =

4. Similar Figures
Similar figures must be the same shape, but their sizes may be different. ~

5. Angles and Sides in Similar Polygons
∠A ≅ ∠ E
∠B ≅ ∠ F
∠C ≅ ∠ G
Sides
AB ~ EF
AC ~ EG
BC ~ FG A
ΔABC ~ ΔEFG E B C F G

6. You can find the missing length of a side in a pair of similar figures, by using proportions
ΔRST ~ ΔUVW R
x ft. U
6 ft. S T W V
35 ft.
7 ft.
x = 30 feet = x 35

7. Solve for x.
40 in.
30 in..
12 in.
x in. x
x = 9 inches = 12 40

8. Solve for x. Round to the nearest tenth.
12 in.
4 in.
20 in.
x in.. x
x = 6.7 inches = 12 20

9. Solve for x. x
25 m.
14 m.
7 m.
x = 50 meters = 14 x

10. Solve for x. Round to the nearest tenth.
17 in. x
35 in.
15 in. x
x = 7.3 inches = 35 17

11. Determine the missing sides of the triangle

12. Determine the length of the missing side
Two rectangles are similar. The first is 4 in. wide and 15 in. long. The second is 9 in. wide. Find the length of the second rectangle.

13. Determine the length of the missing side
Two rectangles are similar. One is 5 cm by 12 cm. The longer side of the second rectangle is 8 cm greater than twice the shorter side. Find its length and width.

14. Similar Figures
Which of the following is not a characteristic of similar figures?
A. Proportional sides B. Equal angle measurements C. Same shape D. Congruent side lengths

15. Similar Figures
Are the figures below similar? Explain.

16. Similar Figures
Are the figures below similar? Explain.