ID: 1
Grade 10 Mathematics
Name___________________________________
Similar Triangles
Date________________
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State if the triangles in each pair are similar. If so, state how you know they are similar and complete the
similarity statement.
1)
2)
C
E
6
5
V
27
9
B
8
D
42
U
V
9
U
F
A
27
35
56
∆ABC ~ ______
T
∆VUT ~ ______
4)
3)
Q
B
50
K
30
39
40
24
51
V
U
C
18
J
27
A
P
36
30
∆CBA ~ ______
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T
∆VUT ~ ______
-1-
Worksheet by Kuta Software LLC
5)
6)
K
40
C
28
52
L
M
T
50
35
65
S
D
L
B
R
∆RST ~ ______
K
∆DCB ~ ______
7)
8)
F
F
50
E
W
S
G
78
E
30
V
130
G
R
∆EFG ~ ______
∆EFG ~ ______
Find the missing length. The triangles in each pair are similar.
9)
10)
G
F
60
?
169
E
C
?
53°
H
60
Q
156
Q
D
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E
110
53°
S
110
R
-2-
Worksheet by Kuta Software LLC
11)
12)
99
B
S
L
54
?
77
C
32
42
C
?
A
K
R
121
13)
Q
32
B
72
14)
S
K
J
33
60
36
R
?
Q
L
10
C
12
?
10
V
U
D
E
15)
16)
B
30
?
R
D
84
D
52
Q
C
T
?
S
42
24
48
168
U
E
84
B
Solve for x. The triangles in each pair are similar.
17)
18)
9 x − 10
50
T
45
72
D
B
U
30
24
Q
18
48
9
12
E
V
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A
6
R
C
x+5
-3-
Worksheet by Kuta Software LLC
19)
20)
C
E
15
3x − 3
3x − 6
D
14
B
6
D
S
P
R
T
14
55
77
Q
R
21)
U
63
22)
H
27
16
N
S
21
M
21 + 2 x
T
12
G
F
Q
6 x + 16
66
R
23)
24)
F
54
T
M
S
20
45
E
P
35
24
30
D
20
8x + 2
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F
K
27
L
x+7
E
-4-
Worksheet by Kuta Software LLC
Answers to Similar Triangles (ID: 1)
1) similar; SAS similarity; ∆AUV
2) similar; SSS similarity; ∆FED
3) similar; SSS similarity; ∆CKJ
4) not similar
5) similar; SSS similarity; ∆MLK
6) not similar
7) similar; AA similarity; ∆EVW
8) similar; SAS similarity; ∆ERS
9) 65
10) 60
11) 66
12) 72
13) 11
14) 60
15) 60
16) 91
17) 10
18) 7
19) 9
20) 3
21) 14
22) 12
23) 5
24) 11
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-5-
Worksheet by Kuta Software LLC
ID: 2
Grade 10 Mathematics
Name___________________________________
Similar Triangles
Date________________
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State if the triangles in each pair are similar. If so, state how you know they are similar and complete the
similarity statement.
1)
2)
W
V
T
S
76°
9
15
G
24
12
R
F
E
76°
∆GFE ~ ______
F
G
∆RST ~ ______
3)
4)
D
45
G
C
8
A
14
T
45
65
U
F
35
C
B
∆ABC ~ ______
S
∆UTS ~ ______
5)
6)
G
8
T
72
F
9
U
L
J
140
126
81
V
45
K
50
∆JKL ~ ______
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F
E
∆VUT ~ ______
-1-
Worksheet by Kuta Software LLC
7)
8)
S
B
8
10
14
U
V
8
A
T
15
6
R
4
3
T
∆VUT ~ ______
F
G
∆RST ~ ______
Find the missing length. The triangles in each pair are similar.
9)
10)
?
K
52
E
13
J
40
44
S
11
88
K
9
J
35
T
L
L
F
?
11)
12)
B
21
V
C
7
T
W
88
13
70
U
?
M
?
U
40
L
V
13)
K
52
G
13
J
8
H
L
?
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-2-
Worksheet by Kuta Software LLC
14)
15)
16
C
E
D
28
B
98
91
? 39
E
?
S
T
18 C
D
F
42
42
R
16)
M
44
?
L
N
55
P
Q
50
R
Solve for x. The triangles in each pair are similar.
17)
18)
T
P
24
36
Q
9 x − 10
U
26
M
K
5x − 6
70
L
S
30
E
42
F
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-3-
Worksheet by Kuta Software LLC
19)
20)
154
4x + 8
J
26
16
88
T
E
40
K
27
143
S
36
D
G
C
−9 + 3 x
L
21)
H
22)
M
R
60
4 x + 17
L
−3 + 3 x
K
F
18
P
72
Q
D
78
G
H
5
3
C
23)
24)
F
60
69°
B
E
55
F
H
54
Q
154
R
72
G
69°
D
13 x − 14
12
N
S
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-4-
x+6
M
Worksheet by Kuta Software LLC
Answers to Similar Triangles (ID: 2)
1) not similar
4) not similar
7) not similar
11) 39
15) 42
19) 5
23) 14
2) similar; AA similarity; ∆RGF
3) not similar
5) similar; SAS similarity; ∆JFG
6) similar; SAS similarity; ∆VEF
8) not similar
9) 36
10) 77
12) 154
13) 32
14) 24
16) 40
17) 12
18) 9
20) 13
21) 12
22) 11
24) 10
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-5-
Worksheet by Kuta Software LLC
ID: 3
Grade 10 Mathematics
Name___________________________________
Similar Triangles
Date________________
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State if the triangles in each pair are similar. If so, state how you know they are similar and complete the
similarity statement.
1)
G
F
2)
30
36
D
C
45
60
108
20
E
K
L
10
27
E
F
∆EFG ~ ______
M
∆KLM ~ ______
3)
4)
F
32°
52
48
32
P
30°
F
Q
56
R
E
∆EFG ~ ______
∆FED ~ ______
5)
S
26°
E
39
36
D
G
6)
N
G
89°
R
92°
H
S
M
L
D
F
∆FGH ~ ______
F
E
∆DEF ~ ______
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-1-
Worksheet by Kuta Software LLC
7)
G
45
8)
55
B
Q
48
L
D 25
F
8
99
C
7
P
R
K
∆DCB ~ ______
49
∆PQR ~ ______
Find the missing length. The triangles in each pair are similar.
9)
10)
D
R
?
Q
R
16
12
C
?
V
26
E
Q
22
65
S
W
20
11)
12)
N
G
E
10
45
?
M
L
?
F
Q
D
48
B
18
22
C
40
R
S
13)
S
C
14)
K
L
?
44
A
16
50
70
T
J
66
?
B
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C
-2-
10
B
Worksheet by Kuta Software LLC
15)
16)
E
D
60
L
M
36
9
11
?
T
104
L
M
48
S
C
?
N
Solve for x. The triangles in each pair are similar.
17)
18)
27
K
B
L
56
24
15
24
M
C
80
G
2x + 7
G
30
F
H
D
70
8x + 2
F
19)
20)
J
42
11
K
S
78
5 x + 18
9
7
E
R
4x + 6
F
D
D
66
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91
E
-3-
91
F
Worksheet by Kuta Software LLC
21)
E
6 + 15 x
22)
K
11
24
M
L
D
13
L
78
26
F
K
V
12
T
23)
24)
Q
11 x + 2
5
18
V
U
16
49
V
U
x
7
T
R
6
W
P
D
42
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2x − 5
E
-4-
8
C
Worksheet by Kuta Software LLC
Answers to Similar Triangles (ID: 3)
1) similar; SAS similarity; ∆ECD 2) not similar
3) similar; SSS similarity; ∆FQP
4) not similar
5) not similar
6) not similar
7) similar; SAS similarity; ∆DGF 8) similar; SAS similarity; ∆PLK
9) 15
10) 55
11) 12
12) 55
13) 24
14) 14
15) 44
16) 130
17) 11
18) 14
19) 12
20) 12
21) 4
22) 13
23) 3
24) 7
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-5-
Worksheet by Kuta Software LLC