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Geometry
Unit 2
Worksheet
Show all work on a separate sheet of work paper. Remember to follow the criteria
for credit.
Use the following diagram for
problems 1 – 3.
Use the following diagram for
problems 7 – 9.
1.
Identify a pair of complementary
angles.
7.
Identify a pair of complementary
angles.
2.
Identify a pair of supplementary
angles.
8.
Identify a pair of supplementary
angles.
3.
Identify a pair of vertical angles.
9.
Identify a pair of vertical angles.
4.
Use the following diagram to
solve for x.
5.
6.
10.
Use the following diagram to
solve for x.
Use the following diagram to
solve for x.
11.
Use the following diagram to
solve for x.
Use the following diagram to
solve for x and y.
12.
Use the following diagram to
solve for x and y.
Page 1 of 10
© Mastery Mathematics
8/11/01
Geometry
Unit 2
Use the following diagram for
problems 13 – 15.
Worksheet
Use the following diagram for
problems 19 – 21.
13.
Identify a pair of complementary
angles.
19.
Identify a pair of complementary
angles.
14.
Identify a pair of supplementary
angles.
20.
Identify a pair of supplementary
angles.
15.
Identify a pair of vertical angles.
21.
Identify a pair of vertical angles.
16.
Use the following diagram to
solve for x.
22.
Use the following diagram to
solve for x.
17.
Use the following diagram to
solve for x.
23.
Use the following diagram to
solve for x.
24.
Use the following diagram to
solve for x and y.
18.
Use the following diagram to
solve for x and y.
Page 2 of 10
© Mastery Mathematics
8/11/01
Geometry
25.
26.
Unit 2
Use the following diagram to
solve for x.
Worksheet
30.
Use the following diagram to
solve for x and y.
31.
Find the circumference to the
nearest tenth.
Use the following diagram to
solve for x.
1 dm
32.
Find the circumference to the
nearest tenth.
3 hm
27.
Use the following diagram to
solve for x and y.
28.
Use the following diagram to
solve for x.
29.
Use the following diagram to
solve for x.
Page 3 of 10
33.
Find the circumference to the
nearest tenth.
34.
Find the circumference to the
nearest tenth.
© Mastery Mathematics
8/11/01
Geometry
Unit 2
35.
Find the circumference to the
nearest tenth.
36.
Find the perimeter.
11 mm
4 mm
Worksheet
41.
Find the perimeter.
42.
Find the perimeter.
43.
Find the area.
6 mm
15 mm
37.
Find the perimeter.
6m
3m
10 m
15 m
38.
3 km
Find the perimeter.
18 hm
5 hm
8 hm
12 hm
44.
39.
Find the area.
Find the perimeter.
8 hm
3 dm
4 dm
40.
Find the perimeter.
45.
Find the area.
4 km
4 cm
6 km
Page 4 of 10
5 cm
© Mastery Mathematics
8/11/01
Geometry
46.
Unit 2
Find the area.
Worksheet
51.
Find the area.
52.
Find the area.
53.
Find the area.
54.
Find the area of a square whose
perimeter is 12 m.
55.
Find the area of a square whose
perimeter is 8 cm.
56.
Find the area of a square whose
perimeter is 32 m.
57.
Find the area of a square whose
perimeter is 36 cm.
6 dm
3 dm
47.
Find the area.
6 mm
7 mm
5 mm
11 mm
48.
Find the area.
5 km
16 km
8 km
12 km
49.
50.
Find the area.
Find the area.
Page 5 of 10
© Mastery Mathematics
8/11/01
Geometry
58.
59.
60.
61.
Unit 2
Find the area of a circle whose
circumference is 6π cm. Leave
your answer in terms of π.
Find the area of a circle whose
circumference is 8π cm. Leave
your answer in terms of π.
Find the area of a circle whose
circumference is 10π cm. Leave
your answer in terms of π.
Find the area of a circle whose
circumference is 12π cm. Leave
your answer in terms of π.
For problems 62 – 67, rewrite the
given statement in if-then form.
Underline the hypothesis once and
the conclusion twice.
62.
An object weighs 16 ounces if it
weighs one pound.
63.
Three points are collinear if they
lie on the same line.
64.
Blue trunkfish live in the waters
of a coral reef.
65.
The measure of a right angle is
90˚.
66.
67.
A line contains at least two
points.
Constrictors, such as pythons,
are not poisonous.
Page 6 of 10
Worksheet
Use the following statement for
problems 68 – 74.
If an angle is a right angle, then it has a
measure of 90˚.
68.
Classify the statement as true or
false.
69.
Write the converse of the given
statement.
70.
Classify the converse as true or
false.
71.
Write the inverse of the given
statement.
72.
Classify the inverse as true or
false.
73.
Write the contrapositive of the
given statement.
74.
Classify the contrapositive as
true or false.
Use the following statement for
problems 75 – 81.
If two angles are supplementary, then
the sum of the angle measures is 180˚.
75.
Classify the statement as true or
false.
76.
Write the converse of the given
statement.
77.
Classify the converse as true or
false.
78.
Write the inverse of the given
statement.
79.
Classify the inverse as true or
false.
80.
Write the contrapositive of the
given statement.
81.
Classify the contrapositive as
true or false.
© Mastery Mathematics
8/11/01
Geometry
Unit 2
Use the following statement for
problems 82 – 88.
Worksheet
92.
If an angle is bisected, then it is divided
into two congruent parts.
82.
83.
Classify the statement as true or
false.
If an angle is acute, then its
measure is 36˚.
93.
Write the converse of the given
statement.
84.
Classify the converse as true or
false.
85.
Write the inverse of the given
statement.
86.
Classify the inverse as true or
false.
87.
Write the contrapositive of the
given statement.
88.
Classify the contrapositive as
true or false.
If you have a job, then you work
only on Saturday.
Page 7 of 10
Points A, B and C are on
plane X.
q: Point D is on plane Y.
97.
Prove that the following
conditional statement is false by
providing a counterexample.
Prove that the following
conditional statement is false by
providing a counterexample.
Using p and q, write q  p
in words.
p:
Prove that the following
conditional statement is false by
providing a counterexample.
If you are in a math class, then
you have math first hour.
91.
Prove that the following
conditional statement is false by
providing a counterexample.
If x > y, then x2 > y2
96.
90.
Prove that the following
conditional statement is false by
providing a counterexample.
If x2 = 25, then x = 5.
95.
If you live in a state east of
Arizona, then you live in Texas.
Prove that the following
conditional statement is false by
providing a counterexample.
If you own an automobile, then
you own a Chevy.
94.
89.
Prove that the following
conditional statement is false by
providing a counterexample.
98.
Using p and q, write ~q  ~p
in words.
p:
Points X, Y and D are on the
same line.
q:
Point W is on the same line
as X and Y.
Using p and q, write p  q
in words.
p:
intersects
at a
point.
q: Point P is the point of
intersection.
© Mastery Mathematics
8/11/01
Geometry
99.
100.
Unit 2
Using p and q, write q  p
in words.
106.
A and B are supplementary.
q: John has the fastest time for
the 100 butterfly.
Therefore,
mA  mB  180 ˚.
Using p and q, write ~p  ~q
in words.
107.
q: Sarah went to the movies.
Using p and q, write
in words.
q: Freshmen want to be like
sophomores.
108.
For problems 102 – 106, state
whether the given argument is valid
or invalid. If it is invalid, briefly
explain why.

An isosceles triangle has at
least two sides with the same
length.

∆XYZ has three sides with
the same length.
If the following two premises
(statements) are true, what
conclusion can you reach?

Points Q, R, S lie within
plane P.

Points Q, S lie on line k.
If it is raining, then my dog gets
wet.
It is raining.
109.
Therefore, my dog is wet.
103.
If the following two premises
(statements) are true, what
conclusion can you reach?
~q
p: Sophomores are the
smartest students on
campus.
102.
If two angles are supplementary,
then their sum is 180˚.
p: John is a good swimmer.
p: Sarah went to the mall.
101.
Worksheet
If mA = 90˚, then A is not
acute.
If the following two premises
(statements) are true, what
conclusion can you reach?

A square has four sides with
the same length and four
angles with the same
measure.

ABCD has four sides with the
same length.
A is not acute.
Therefore, mA = 90˚.
104.
If it is a cat, then it is an animal.
Whiskers is an animal.
Therefore, Whiskers is a cat.
105.
If M is the midpoint of AC, then
AM = MC
M is the midpoint of AC.
110.
Find the next two terms for the
given sequence and describe the
pattern for the sequence.
1, 3, 7, 15, 31, …
Therefore, AM = MC.
Page 8 of 10
© Mastery Mathematics
8/11/01
Geometry
111.
Unit 2
Find the next two terms for the
given sequence and describe the
pattern for the sequence.
120.
Find the distance between the
point A( 5, 8 ) and point
B( -2, 3 ). Round your answer to
the nearest tenth.
121.
Find the distance between the
point E( -3.5, -2 ) and point
F( 3.5, 6 ). Round your answer
to the nearest tenth.
122.
Find the distance between the
point B( 3, -1 ) and point
C( 0, 3 ). Round your answer to
the nearest tenth.
123.
Find the distance between the
point E( 3, -3 ) and point
D( -2, -1 ). Round your answer
to the nearest tenth.
124.
Find the distance between the
point J( 1, 4 ) and point K( -2, 3 ).
Round your answer to the
nearest tenth.
125.
Find the midpoint of the segment
formed by point X( 4, 5 ) and
point Y( -1, 3 ).
1, 6, 11, 16, 21, …
112.
Find the next two terms for the
given sequence and describe the
pattern for the sequence.
1, 3, 4, 7, 11, …
113.
Find the next two terms for the
given sequence and describe the
pattern for the sequence.
0, 3, 8, 15, …
114.
Find the next two terms for the
given sequence and describe the
pattern for the sequence.
1, 2, 5, 10, 17, 26, …
115.
Worksheet
Find the next two terms for the
given sequence and describe the
pattern for the sequence.
3, -12, 48, -192, …
116.
Sketch the points M, N and P
such that M and P are collinear
and N is non-collinear.
126.
Find the midpoint of the segment
formed by point A( 5, 8 ) and
point B( -2, 3 ).
117.
Sketch the points T, U and V
such that T and U are collinear
and V is non-collinear.
127.
Find the midpoint of the segment
formed point E( -3.5, -2 ) and
point F( 3.5, 6 ).
118.
Sketch the points P, Q and R
such that Q and R are collinear
and P is non-collinear.
128.
Find the midpoint of the segment
formed by point B( 3, -1 ) and
point C( 0, 3 ).
129.
Find the midpoint of the segment
formed by point E( 3, -3 ) and
point D( -2, -1 ).
130.
Find the midpoint of the segment
formed by point J( 1, 4 ) and
point K( -2, 3 ).
119.
Find the distance between the
point X( 4, 5 ) and point
Y( -1, 3 ). Round your answer to
the nearest tenth.
Page 9 of 10
© Mastery Mathematics
8/11/01
Geometry
131.
Unit 2
In the diagram below,
bisects ABC . If mDBC = 32˚
and mABC = (6x + 4)˚, find x.
135.
Worksheet
In the diagram below,
bisects LMN .
If mLMP = (2x – 27)˚
and mNMP = (5x – 45)˚, find x.
A
L
M
B
D
P
C
132.
In the diagram below,
bisects XYZ .
If mXYZ = (2x + 24)˚
and mXYW = 30˚, find x.
136.
N
In the diagram below,
bisects KAR . If mTAK = 27 ˚
and mKAR = (7x – 9)˚, find x.
Y
X
Z
W
133.
In the diagram below,
bisects QRS .
If mQRT = (4x – 28)˚ and
mSRT = (12x – 36)˚, find x.
Q
T
R
S
134.
In the diagram below,
bisects MAT .
If mMAT = (8x – 6)˚ and
mMAH = 45˚, find x.
H
M
A
Page 10 of 10
T
© Mastery Mathematics
8/11/01