Similar Polygons

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
Angles ?A ? ? E ?B ? ? F ?C ? ? G
Sides AB EF AC EG BC FG
A
?ABC ?EFG
E
B
C
F
G
6
You can find the missing length of a side in a
pair of similar figures, by using proportions
?RST ?UVW
R
U
x ft.
6 ft.
S
T
W
V
35 ft.
7 ft.
6 7
x 30 feet

x
35
7
Solve for x.
40 in.
30 in..
12 in.
x in.
x 30
x 9 inches

12
40
8
Solve for x. Round to the nearest tenth.
12 in.
4 in.
20 in.
x in..
4 x
x 6.7 inches

12
20
9
Solve for x.
x
25 m.
14 m.
7 m.
7 25
x 50 meters

x
14
10
Solve for x. Round to the nearest tenth.
17 in.
x
35 in.
15 in.
15 x
x 7.3 inches

35
17
11
Determine the missing sides of the triangle
39 in
? in
33 in
? in
8 in
24 in
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 sidesB. Equal
angle measurementsC. Same shapeD. Congruent
side lengths
15
Similar Figures

• Are the figures below similar? Explain.

16
Similar Figures

• Are the figures below similar? Explain.