Name: _______________________________________________ Period: _________
Unit 4: Similarity
Geometry
Homework
Section 4.1: Similar Polygons
Are the polygons similar? If they are, write a similarity statement, and give the similarity ratio. If they are not,
explain.
K
T
16
8
A
8
1. X 4 Y
2. B
3. J
K
S
6
K
9
9
4
N
W
4.
3
A
B
Y
5
3
12
4
C
M
6
X
5
M
M
21
20
3
M
8
8
60°
20
3
5
S
N
3
120°
U
8
6
5
10
12
Y
Z
7
6
T
B
C
14
J
LMNO ~ HIJK. Complete the proportions and congruence statements.
7. ∠M ≅ ____
8. ∠K ≅ ____
9. ∠N ≅ ____
10. MN =
IJ JK
11. HK = HI
LM
M
12. IJ =
MN NO
K
N
O
L
I
H
The polygons are similar. Find the values of the variables.
Q
13. P
14. J
L
M
5 in.
S
8 in.
15.
3 in.
R
B
6 ft
15 m
16.
G
C
M
N
P
Q
6m
S
L
3.3 ft
E
x
F
∆WXZ ~ ∆DFG. Use the diagram to find the following.
17. The similarity ratio of ∆WXZ and ∆DFG
18. m∠Z
19. DG
5
20. GF
21. m∠G
37°
W
22. m∠D
4
x
H
F
Y 1.5 cm
Z
X
W
10 cm
E
4 cm
G
Z
3
X
D
R
9m
G
5 ft
A
x
O
K
x
6
F
8
X
A
4
4
R
L
8
6.
R
Z
C
8
Q
5.
3
60°
120°
35
20
N
Z
4
5
L
Section 4.2: Proving Triangles Similar
For questions 1 – 9, determine if the triangles are similar. If they are, find the following:
A) Tell how they are similar
B) Find the scale factor
C) Write the similarity statement
N
X 76°
A
1. J
2. Q 2
3. M
4.
5.
15
3
76°
K
48°
63°
Z
R
U
Y
6
O
S
26
26
13
7
K
13
N
O
M
L
J
Q
T
L
P
B
L
30
E
C
D
6.
U
10
T
W
5
X
14
V
28
7.
M
8.
A
9. E
P
L
O
25
N
B
D
I
50
E
H
40
G 20
C
Solve each word problem by making a sketch.
10. A 6 ft tall tent standing next to a
11. A map has a scale of 3 cm : 18
cardboard box casts a 9 ft
km. If Riverside and Smithville
shadow. If the cardboard box
are 54 km apart then they are
casts a shadow that is 6 ft long
how far apart on the map?
then how tall is it?
Complete the following proofs.
13. GIVEN: ∠S ≅ ∠W
PROVE: ∆SUV ~ ∆TUV
T
S
14. GIVEN: RM ║ SN, RM ⟂MS, SN ⟂ NT
PROVE: ∆RSM ~ ∆STN
R
S
U
V
12. A 6 ft tall car standing next to
an adult elephant casts a 30 ft
shadow. If the adult elephant
casts a shadow that is 51.5 ft
long then how tall is it?
M
W
T
N
Review
Name the type of angle pair relationship and find the value of the variable.
1.
2.
3.
4.
F
Section 4.3: Similar Right Triangles
Draw the 3 similar triangles and find the value of their variables. Leave answers as simplified radicals.
1.
2.
3.
x
4
x
10
5.
6.
81
100
x
7
9
8.
y
z
3
9.
9
x
14
y
1
y
8
11.
x
12
x
16
84
x
6
x
45
x
36
7.
10.
60
25
9
4.
36
x
12
x
12.
y
x
y
z
6
2
Review
Is the statement always, sometimes, or never true?
1.  When there is a transversal that intersects two lines, the three lines are coplanar.
2.  Two lines that are not coplanar intersect.
3.  Two planes parallel to the same plane are parallel to each other.
4.  Two lines intersect at a point.
5.  Two skew lines are parallel.
6.  A transversal intersects two lines.
7.  If parallel lines are cut by a transversal then the alternate interior angles are not congruent.
8.  A theorem can be proven.
Section 4.4: Proportions in Triangles
Solve for x.
2
1.
2.
5
x
6
3.
3
6
4
x
9
5.
6.
7.
12
16
3x
10.
x
x+2
x+4
3
8.
4
20
9
x+1
x
12
15
7.5 2.5x
11.
8
10
8
12.
16
6
2x
7
10
9
x+7
x
Use the figure to complete each proportion.
12. a =
13.
14.
= e
c
f
c
f
a =
b
e
a
b
15. f = c
e
x
3
4
3
9
x
9.
4. 8
x
5
16. a = b
e
17.
Review
Draw and label a figure for each relationship.
1.  AB is in plane Q.
2.  ST intersects AB at P.
3.  Point X is collinear with point A and P.
4.  Point Y is not collinear with points T and P.
5.  Line L contains points X and Y.
e = f
c
c
d
e
f
x-4
x
Geometry Unit 4 Practice TEST
The polygons are similar. Find the value of each variable. [4 points]
1. ΔABC ~ ΔFED
2.ΔRQF ~ ΔGFH
A
Q
7x+6
77
C
B
11x+11
R
D
F
65
169
G
30
H
143
E
F
21
F
Find the value of the variables. Leave answers as simplified fractions or radicals where applicable. [4
points]
4.
6
3.
2
1
9
2
x
x
8
5.
6.
15
x
15
20
x
8
7.
24
8. x
3
25
x+ 1
9
6
x
2
9.
x
10.
y
4
x
12
1
y
z
2
11. A person 5.8 ft tall casts a shadow 12.2 ft long. At the same time, a building casts a shadow 120 ft long. How tall is the building? ROUND
the answer to one decimal place. [5 points each]
12. A map has a scale of 3 cm : 10 mi. If Clayton and Centerville are 12.2 cm apart on the map, how far apart are the real cities? ROUND
the answer to one decimal place. [5 points each]
State if the triangles are similar. If so, state how you know they similar and write a similarity statement. [5 points each]
U
13.
14.
15.
88
16
K
B
84
25
49
R
L
107
F
70
30
25
S
v
Complete each proof.
16.
ON
Given: MN =
, ∠N ≅ ∠R
PR QR
Prove: ∆MNO ~ ∆PQR
42
T
15
L
S
T
R
Q
28
U
A
B
D
U
N
V
18. Given: AB 11 DC
Prove: ∆ABE ~ ∆DCE
17. Given: ∠W ≅ ∠S
Prove: ∆SUV ~ ∆TUW
P
8
Q
M
O
14
M
M
T
V
C
E
W