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Similar Figures
Contributed by: Terman
(Original author: Warren)
Similar Figures
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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?
IJ
Which side corresponds to LM?
10
HI
HK
N
M
4
H
K
MN
8
I
J
3
L
O
Is rectangle LMNO similar to rectangle HIJK?
HI
Which side corresponds to MN?
10
NO
IJ
N
M
4
H
K
JK
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
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