Transcript Similar Figures


Similar figures have the same shape, but not
necessarily the same size.
60°
60°
The ratio formed by the
sides is the scale factor:
14m = 2m
7m
1m
A
12 cm
N
B
1.
2.
3.
4.
5.
P
X
M
∆ABC is similar to ∆NMP.
Find the length of X.
C
Set up a proportion: Large ∆ to Small ∆
Large ∆ 15 = 12
Small ∆ 5
x
Cross multiply and solve.
15x = 60
x=4
The missing length of ∆NMP is 4 cm.
H
J
Trapezoid DEFG is similar to trapezoid HJKL.
E
D
Find the length of side LK.
8 cm
G
1.
2.
3.
4.
5.
10 cm
F
L
K
Set up a proportion: Small trapezoid to Large trapezoid
Small 8 = 10
Large 15 x
Cross multiply and solve.
8x = 150
x = 18.75
The length of LK is 18.75 cm.
F
1.
2.
3.
4.
5.
6.
6m
B
R S
8m
20 m
A
C
12 m
D
Polygon ABCDEF is similar to
polygon RSTUVW.
Find the lengths of RS and WV.
TU
W
V
E
Set up a proportion: Large
polygon to Small polygon
Large 20 = 6
Small 8
x (RS)
Cross multiply and solve.
20x = 48
x = 2.4
The length of RS is 2.4 m.
1.
2.
3.
4.
5.
6.
Set up a proportion: Large
polygon to Small polygon
Large 20 = 12
Small 8
x (WV)
Cross multiply and solve.
20x = 96
x = 4.8
The length of WV is 4.8 m.
A picture 10 in. tall and 14 in. wide is to be scaled to 1.5 in. tall
to be displayed on a Web page. How wide should the picture
be on the Web page for the two pictures to be similar?
Step 1: Draw & Label a picture.
Step 2: Set up a proportion.
1.5 in.
10 in.
? in.
14 in.
Large 10 = 14
Small 1.5
x
14(1.5) = 10x
21 = 10x
The picture should be 2.1 in. wide.
A flag in the shape of an isosceles triangle with side lengths 18
ft, 18 ft, and 24 ft is hanging on a pole outside a campground. A
camp t-shirt shows a smaller version of the triangle with two
sides that are each 4 in. long. What is the length of the third
24ft
side of the triangle on the t-shirt?
Set up a proportion.
18 ft =
4 in.
24 ft
x in.
18 ft
18 ft • x in. = 24 ft • 4 in. Find the cross products.
18x = 96
Multiply
x =96  5.3
Solve for x.
18
The third side of the triangle is about 5.3 in. long.
18ft
8 ft
A
4 ft
6 ft
B
3 ft
5 ft
C
2 ft
Since the three figures are all rectangles, all the
angles are right angles. So the corresponding
angles are congruent.
Compare the ratios of corresponding sides to see if
they are equal.
8 ft
A
6 ft
4 ft
length of rectangle A
length of rectangle B
B
3 ft
8 ?4
=
6 3
24 = 24
5 ft
C
2 ft
width of rectangle A
width of rectangle B
The ratios are equal. Rectangle A is similar to
rectangle B. The notation A ~ B shows
similarity.
8 ft
A
6 ft
4 ft
length of rectangle A
length of rectangle C
B
3 ft
8 ? 4
=
5 2
16  20
5 ft
C
2 ft
width of rectangle A
width of rectangle C
The ratios are NOT equal. Rectangle A is NOT
similar to rectangle C.