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Similar Figures
Contributed by: Davies
(Original author: Warren)
Similar Figures
|||
What is the simplified form of all of these ratios?
because the ratios of their matching sides
were equal.
In the last example, the triangles were similar
15
10
=
12
8
=
9
6
=
L
O
Is rectangle LMNO similar to rectangle HIJK?
10
N
M
4
H
K
8
I
J
3
L
O
Is rectangle LMNO similar to rectangle HIJK?
1. Are the corresponding (matching)
10
angles the same size?
Yes.
N
M
4
No.
H
K
8
I
J
3
L
O
Is rectangle LMNO similar to rectangle HIJK?
1. Are the corresponding (matching)
2. Are the corresponding (matching) sides
in the same ratio?
angles the same size?
10
Yes.
N
M
4
H
K
8
I
J
3
L
O
Is rectangle LMNO similar to rectangle HIJK?
Which side corresponds to LM?
10
N
M
4
H
K
8
I
J
3
L
O
Is rectangle LMNO similar to rectangle HIJK?
Which side corresponds to MN?
10
N
M
4
H
K
8
I
J
3
L
O
Is rectangle LMNO similar to rectangle HIJK?
Write the unsimplified ratio of LM to HI:
10
N
M
4
H
K
8
I
J
3
L
O
Is rectangle LMNO similar to rectangle HIJK?
Write the ratio of MN to IJ:
10
N
M
4
H
K
8
I
J
3
L
O
Is rectangle LMNO similar to rectangle HIJK?
Is the ratio LM:HI equal to the ratio MN:IJ ?
10
10
8
=
N
M
4
4
3
H
K
??
Yes
No
8
I
J
3
L
O
Now answer the question:
Is rectangle LMNO similar to rectangle HIJK?
10
Yes
No
N
M
4
H
K
8
I
J
3
L
4
O
1. The angles are equal, but
2. The sides are not in the same ratio.
Is rectangle LMNO similar to rectangle HIJK?
Now answer the question:
10
10
NO! 
N
M
4
3
H
K
8
8
I
J
3
A
8
60
B
Is parallelogram ABCD similar to
parallelogram KLMN?
120o
12
12
120
D
60o
8
C
K
4
60
L
120
6
120
6
60
N
4
M
A
8
60
1. Are the corresponding angles equal?
B
Is parallelogram ABCD similar to
parallelogram KLMN?
120
12
12
120
Yes.
No.
D
60
8
C
K
4
60
L
120
6
120
6
60
N
4
M
2. Do the sides form the same ratio ?
A
parallelogram KLMN?
Is parallelogram ABCD similar to
8
60
Complete this ratio:
B
120
12
12
120
D
60
8
C
AB
KL
K
4
60
=
L
120
6
120
6
60
N
4
M
A
2. Do the sides form the same ratio?
parallelogram KLMN?
Is parallelogram ABCD similar to
8
60
Complete this ratio:
B
120
12
12
120
D
60
8
C
LM
BC
K
4
60
=
L
120
6
120
6
60
N
4
M
2. Do the sides form the same ratio ?
Is parallelogram ABCD similar to
A
Are the ratios equal ?
Yes.
8
60
B
120
12
No.
12
120
D
60
8
C
8
4
K
4
60
parallelogram KLMN?
=
L
120
6
12
6
120
6
60
N
4
M
Is parallelogram ABCD similar to
A
8
60
B
120
12
Yes.
12
120
D
No.
60
8
C
K
4
60
parallelogram KLMN?
L
120
6
120
6
60
N
4
M
Is parallelogram ABCD similar to
A
YES!! Corresponding angles are equal AND
corresponding sides are in the same ratio.
8
60
B
120
12
12
120
D
60
8
C
K
4
parallelogram KLMN?
60
L
120
6
120
6
60
N
4
M
Which side corresponds to YZ?
CD
AB
AD
XW
Complete the ratio:
YZ
2
=
Solve this simple equation
to find the length of YZ.
YZ
2
=
16
24
YZ = 
24
D
A
12
C
B
15
Given that
trapezoid ABCD ||| trapezoid WZYX,
find m.   (||| means 'similar to')
W
m
Z
16
Y
X
24
D
A
Given that
find m.
12
C
B
15
Complete the ratio needed to find m:
trapezoid ABCD ||| trapezoid WZYX,
W
m
24
16
Z
16
=
Y
X
m goes here
24
D
A
12
C
B
15
Given that
trapezoid ABCD ||| trapezoid WZYX,
find m.
W
m
Use cross multiplication or 
equivalent fractions to find m.
24
16
Z
=
16
12
m
m =
Y
X
24
D
A
12
C
B
15
Given that
trapezoid ABCD ||| trapezoid WZYX,
find YZ.
W
m
Complete the ratio for YZ:
Z
16
Y
X
Write a number here.
YZ
24
D
A
12
C
B
15
W
Given that
trapezoid ABCD ||| trapezoid WZYX,
find YZ.
Complete the ratio:
m
Z
16
YZ
15
Y
X
=
24
D
A
12
C
B
15
Given that
trapezoid ABCD ||| trapezoid WZYX,
find YZ.
W
15
YZ
m
=
Z
16
24
16
YZ = 
Y
X
C
Given ∆ABC ||| ∆DEF, find n.
12
10
A
B
F
6
n
D
E
Complete this ratio:
C
Given ∆ABC ||| ∆DEF, find n.
12
10
A
B
10
F
n
6
n
=
D
E
C
12
Given ∆ABC ||| ∆DEF, find n.
10
A
B
Solve this ratio:
F
6
n
D
E
10
n
n = 
=
12
6
Congratulations!!
You have finished.
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