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Geometry
Unit 4
Worksheet
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For problems 1-6, Sketch a triangle to fit the
description. If not possible, write Not Possible.
16.
y°
130°
x°
1. Sketch a right isosceles triangle.
2. Sketch an obtuse isosceles triangle.
118°
17.
3. Sketch an acute scalene triangle.
x°
y°
4. Sketch an acute equilateral triangle.
5. Sketch a right equilateral triangle.
18.
6. Sketch a right scalene triangle.
42°
7. A triangle with no sides congruent is a(n)
_____________ triangle.
y°
x°
8. A triangle with all sides congruent is a(n)
_____________ triangle.
19.
58°
y°
9. A triangle with at least two sides congruent
is a(n) _________ triangle.
10. A triangle with a 90 angle is a(n)
_________ triangle.
x°
20.
y°
11. A triangle with two 40 angle is a(n)
_________ triangle.
x°
50°
12. A triangle with three equal angles is a(n)
_________ triangle.
13. A triangle with 40, 60, 80 angles is a(n)
_________ triangle.
21.
y°
26°
x°
For problems 14 – 21, using the given
information in the drawing, find the values of x
and y.
For problems 22 – 26, find the measures of the
angles of the triangle.
x°
14.
140°
y°
22.
15.
x°
95°
(2x – 13)°
(x + 5)°
x°
y°
Page 1 of 9
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Geometry
Unit 4
For problems 23 – 26, find the measures of the
angles of the triangle.
Worksheet
M
N
30.
(x – 44)°
23.
O
P
W
31.
(2x – 72)°
3"
x°
3"
Z
X
24.
x°
(3x + 14)°
(4 x
–
Y
°
1 8)
32.
D
A
C
10 cm
10 cm
25.
B
(2x)°
33.
(8x – 15)°
A
(x + 8)°
B
C
26.
(3x – 21)°
E
(5x +3)°
x°
For questions 27 – 56, decide which
congruence postulate you can use to prove
that the given triangles are congruent. If so,
write the congruence statement and identify
the postulate. If not, write Not Possible.
27.
D
A
34.
A
B
4m
C
4m
D
35.
E
A
B
C
D
D
E
C
B
36.
E
28.
A
B
4 cm
4 cm
C
X
D
4 cm
4 cm
W
37.
O
N
P
Z
Y
E
M
Q
29.
R
3"
S
T
C
2"
2"
3"
B
A
R
X
38.
W
B
M
A
Page 2 of 9
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Geometry
Unit 4
For questions 39 – 56, decide which
congruence postulate you can use to prove
that the given triangles are congruent. If so,
write the congruence statement and identify
the postulate. If not, write Not Possible.
4 cm
47.
R
T
4 cm
S
Y
48. W
K
39.
Worksheet
U
Z
X
M
L
40.
49.
N
A
H
C
D
O
C
41.
X
50.
O
H
O
Y
51.
3 mm
2" W
A
3"
A
D
R
3"
E
B
T
M 2" N
D
A
3 mm
C
T
Y
B
42.
D
A
C
43.
B
E
F
52.
53.
E
J
10 cm
D
B
A
D
O
7 cm
G
B
A
R
T
7 cm
10 cm
A
C
D
44.
X
54.
C
I
C
W
Y
T
Z
A
45.
M
55.
R
T
O
U
G
3 mm
3 mm
S
D
A
56.
46.
32"
P
T
B
A
C
I
G
32"
J
D
Page 3 of 9
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Geometry
Unit 4
Competency 3:
Worksheet
64.
For questions 57 - 68, identify the congruent
triangles from the given drawings, and state
how you know that they are congruent.
R
X
Z
Y
65. A
C
B
A
57.
E
B
D
66. R
C
D
U
E
58.
T
M
L
S
F
67.
N
E
G
O
59. A
H
B
68. L
M
P
C
D
O
N
60.
R
S
For questions 69 - 80, state one additional fact
that is needed for the pair of triangles to be
congruent. State why they would be congruent.
Q
I
69.
T
B
61.
H
J
A
C
K
D
62.
70. M
M
L
N
O
63.
R
Q
N
71.
O
C
S
F
B
E
A
C
D
G
D
Page 4 of 9
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Geometry
72.
Unit 4
M
O
N
P
For questions 81 – 86, copy the given figure
and mark any parts that are equal in measure.
Identify how you would prove the triangles
congruent.
A
73.
Worksheet
81. Given: MK bisects JML,
JKM  LKM
B
M
D
C
M
74.
R
J
O
N
K
82. Given: AB  AD , BC  CD , AB  CD
T
S
A
B
D
C
B
75.
A
C
D
76.
B
4
1
A
77.
83. Given: EF  HG , EH  FG
E
3
E
F
H
G
2
C
D
F
Y
E
84. Given: NQ  OP , QO
Z
D
X
Q
P
N
O
F
78.
G
Q
H
P
F
79.
L
R
85. Given: BD is the  bisector of AC
D
C
A
H
M
B
I
K
L
J
86. Given: RT  ST , U is midpoint of RS
R
80.
D
A
T
U
C
B
E
S
Page 5 of 9
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Geometry
Unit 4
Worksheet
90. Given: AB  CD , BC  AD
Prove: AB  CD
Competency 4: Using Congruence in
Applications
Questions 87 – 92: For the partial proofs below
supply the missing statements or reasons.
87. Given: FH bisects GFJ and GHJ
Prove:  GFH   JFH
2
1
3
4
H
J
Statement
1. FH bisects GFJ
and GHJ
2. 21
3.
4.  GFH   JFH
Reason
1. Given
Statement
1. AB  DE ,
BC  EF ,
AC  DF
2. ABC  DEF
3.
2. Reflexive Property 
3. SSS
4.
5.
E
C
D
Statement
1. BC  EC ,
AC  DC
2. ACBDCE
3. ABC  DEC
D
F
E
Reason
1. Given
2.
3.
92. Given: AB  CB ,
BD is a median of ABC
Prove: ABD  CBD
B
2.
3. CPCTC
D
A
Statement
1. AB  CB ,
BD is a median of
ABC
2.
M
H
Statement
1. HJ  KJ , MJK  MJK
2. MJ  MJ
3. MJH  MJK
Reason
1. Given
C
89. Given: HJ  KJ ,
MJH  MJK
Prove: MJH  MJK
Page 6 of 9
Reason
1. Given
B
Prove: A  D
C
D
A
88. Given: AB  DE , BC  EF , AC  DF
B
A
91. Given: BC  EC , AC  DC
Prove: ABC  DEC
2. If a seg. bisects
an , it divides
it into 2 s
3. Same as 2.
4.
A
C
Statement
1. AB  CD ,
BC  AD
2.
3. BAD  DCB
4. ABDBDC
5. AB  CD
G
F
B
J
Reason
1. Given
2.
3.
K
3.
4. ADB  CDB
5. ADB  CDB
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Reason
1. Given
2. A median divides a 
into 2  segments
3. Reflexive property 
4.
5. CPCTC
update
Geometry
Unit 4
Competency 5: Isosceles, Equilateral
Triangles
Worksheet
For problems 93 – 119, Use the information
provided in the drawing to find x and/or y.
93.
x°
101.
y°
102.
70°
x°
y°
y°
x°
103.
94.
x°
y°
5 0°
x°
y°
95.
104.
y°
3 9°
96.
90"
x°
12x
x°
1 30 °
105.
75 cm
6x
y°
97.
x°
106.
66'
y°
6 0°
10x
98.
y°
107.
x°
5x
80 m
99.
y°
x°
108.
100.
20x
y°
146"
x°
Page 7 of 9
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Geometry
109.
Unit 4
117. In the diagram below, a  b. Find
m 1 and m2, if m1 = 13x and
m2 = 7x + 60.
y°
83°
Worksheet
x°
t
a
110.
x°
1
48°
2
b
y°
111.
118. In the diagram below, a  b. Find
m 1 and m2, if m1 = n + 8 and
m2 = 2n + 3.
y°
59°
x°
t
112.
a
x°
8 8°
1
b
2
y°
113
x°
5 5°
y°
119. In the diagram below, a  b. Find
m 1 and m2, if m1 = 5a and
m2 = 2a + 12.
t
a
1
Competency 6: Distributed Practice
114. In the diagram below, a  b. Find
m 1 and m2, if m1 = 4k – 8 and
m2 = k + 28.
t
a
2
1
b
2
120. Find the slope of the line parallel to the
graph of
4
2
xy – .
3
3
b
121. Find the slope of the line perpendicular
to the graph of 3x + y = –5.
115. In the diagram below, a  b. Find
m 1 and m2, if m 1 = 6p + 9 and
m2 = 2p + 11.
t
a
2
b
1
116. In the diagram below, a  b. Find
m 1 and m 2, if m1 = 6x + 7 and
m2 = 4x + 47
t
a
b
Page 8 of 9
122. Find the slope of the line parallel to the
graph of 3x + y = –5.
123. Find the slope of the line perpendicular to
the graph of 2x + y = 1.
124. Find the slope of the line parallel to the
graph of –3x + y = –1.
125. Find the slope of the line perpendicular to
the graph of
2
x + y = 4.
7
1
2
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Geometry
Unit 4
For questions 126-131, the figures in the
drawings are right rectangular prisms or
right rectangular pyramids.
Worksheet
133. Write the equation of a line that has a
y-intercept of 9 and is perpendicular to
1
the graph of y = – x.
4
E
126. Using the drawing
to the right, name
two lines that are
skew to BC .
B
X
A
D
135. Write the equation of a line that has a
y-intercept of –5 and is perpendicular to
the graph of y = 5x.
C
Y
Z
136. Write the equation of a line that has a
y-intercept of –4 and is parallel to the
C
M
127. Using the drawing
to the right, name
two lines that are
parallel to GB .
134. Write the equation of a line that has a
y-intercept of 6 and is parallel to the
graph of y = 9x.
2
A
graph of y = – x.
E
3
N
137. Write the equation of a line that has a
y-intercept of 3 and is perpendicular to
the graph of y = –3x.
B
L
G
M
L
P
N
K
129. Using the drawing
to the right, name
all the lines that are
parallel to PO .
138. A square has four congruent sides.
Polygon ABCD has four congruent sides.
Therefore, polygon ABCD is a square.
R
139. If it is raining outside, practice will be
cancelled. It is not raining outside.
Therefore, practice will not be cancelled.
Q
N
P
O
140. If there are clouds in the sky, we will not
go sailing. There are clouds in the sky.
Therefore, we will not go sailing.
W
130. Using the drawing
to the right, name
two lines that are
perpendicular to SV .
V
S
U
141. If a number is divisible by 10 then it is
divisible by 5. 100 is divisible by 10.
Therefore, 100 is divisible by 5.
Q
142. If a number is divisible by 6 then it is
divisible by 3. 33 is not divisible by 6.
Therefore, 33 is not divisible by 3.
T
131. Using the drawing
U
to the right, name
two lines that are
skew to PQ .
V
State whether the following arguments are
valid or invalid. If it’s invalid, briefly explain
why.
O
128. Using the drawing
I
to the right, name
two lines that are
perpendicular to JK . J
P
T
I
R
S
132. Write the equation of a line that has a
y-intercept of –2 and is parallel to the
143. If there is a teacher’s meeting, students
are dismissed early. Today there is a
teacher’s meeting. Therefore, students
are dismissed early today.
2
graph of y = x.
5
Page 9 of 9
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