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Name:_______________________
Midterm
Date:_______________________
______________________________________________________________________________
1
To prove
in the diagram below, you write the given information that
. What are the next two statements you should write in the proof?
2
A
Corresponding Parts of Congruent Triangles
SAS Postulate
B
Vertical Angles
ASA Postulate
C
Vertical Angles
Corresponding Parts of Congruent Triangles
D
Corresponding Parts of Congruent Triangles
Corresponding Parts of Congruent Triangles
Which statement, if any, can you prove based on the figure below?
A
B
C
D
3
None of the above
Both choices A and B
Choose the converse of the following true conditional statement. If the converse is also
true, combine the statements as a biconditional.
If x = 3, then x2 = 9.
A
B
C
D
If x2 = 9, then x = 3. True; x2 = 9 if and only if x = 3.
If x2 = 3, then x = 9. False
If x2 = 9, then x = 3. True; x = 3 if and only if x2 = 9.
If x2 = 9, then x = 3. False
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Page 1 of 21
Midterm
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4
Using the Law of Syllogism, what conclusion can you draw from the two given statements?
If a number is a multiple of 64, then it is a multiple of 8.
If a number is a multiple of 8, then it is a multiple of 2.
A
B
C
D
5
If a number is a multiple of 64, then it is a multiple of 2.
The number is a multiple of 2.
The number is a multiple of 8.
If a number is not a multiple of 2, then the number is not a multiple of 64.
Which diagram shows plane PQR and plane QRS intersecting only in
?
A
B
C
D
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Page 2 of 21
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6
What is the ray that is opposite
?
A
B
C
D
7
Segment BD bisects angle ABC.
Angle ABC = (7x).
Angle ABD = (3x + 5).
Find angle DBC.
A
B
C
D
8
10
70
105
35
If
scale.
A
B
C
D
find the values of x, EF, and FG. The drawing is not to
x =10, EF = 8, FG = 15
x =3, EF = –6, FG = –6
x =10, EF = 32, FG = 45
x =3, EF = 8, FG = 15
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Page 3 of 21
Midterm
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9
T is the midpoint of the following.
Find the values of x and ST.
A
B
C
D
10
x
x
x
x
= 5, ST = 45
= 5, ST = 60
= 10, ST = 60
= 10, ST = 45
This diagram of airport runway intersections shows two parallel runways. A taxiway
crosses both runways.
How are
A
B
C
D
and
related?
same-side interior angles
alternate interior angles
corresponding angles
none of these
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Page 4 of 21
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11
Find the value of the variable if
scale.
A
B
C
D
12
Find
and
The diagram is not to
1
2
3
0.5
The diagram is not to scale.
A
B
C
D
70
120
110
60
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Page 5 of 21
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13
Which is a correct two-column proof?
Given:
Prove:
and
are supplementary.
A
B
C
D
none of these
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Page 6 of 21
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14
Find the values of x and y.
A
B
C
D
15
x
x
x
x
= 77, y = 59
= 77, y = 57
= 57, y = 77
= 41, y = 57
Find the values of x and y.
A
B
C
D
x
x
x
x
= 15, y = 17
= 112, y = 68
= 68, y = 112
= 17, y = 15
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Page 7 of 21
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16
What can you conclude from the information in the diagram?
A
B
17
are vertical angles
1.
2.
3.
are adjacent angles
C
1.
2.
3.
is a right angle
are vertical angles
D
1.
2.
3.
is a right angle
are adjacent angles
Angle DFG and angle JKL are complementary angles. The measure of angle DFG = (x + 5),
and angle JKL = (x – 9). Find the measure of each angle.
A
B
C
D
18
1.
2.
3.
= 47,
= 47,
= 52,
= 52,
= 53
= 43
= 48
= 38
Angle 1 and 2 are supplementary angles.
Find the measure of each angle.
A
B
C
D
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Page 8 of 21
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19
MO bisects angle LMN. Angle LMO = 8x – 23.
Angle NMO = 2x + 37
Solve for x and find angle LMN.
A
B
C
D
20
= 9,
= 9,
= 10,
= 10,
Is the line through points P(0, 5) and Q(–1, 8) parallel to the line through points R(3, 3) and
S(5, –1)? Explain.
A
B
C
D
21
x
x
x
x
No, the lines have unequal slopes.
Yes, the lines are both vertical.
Yes, the lines have equal slopes.
No, one line has zero slope, the other has no slope.
Which equation describes the line parallel to y = –7x + 15 that contains P(9, –6)?
A
B
C
D
x+6=
(y – 9)
y + 6 = (x – 9)
y – 6 = –7(x – 9)
y + 6 = –7(x – 9)
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Page 9 of 21
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22
Find the slope of a line that is perpendicular to
P(–5, –3), Q(–2, 8)
.
A
B
C
D
23
Use the information in the figure. Find
A
B
C
D
24
64°
122°
32°
58°
Find the value of x.
A
B
C
D
none of these
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Page 10 of 21
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25
Find the value of the variable.
A
B
C
D
26
66
19
29
43
Find the values of x, y, and z.
A
B
C
D
27
Based on the pattern, what are the next two terms of the sequence?
,...
A
B
C
D
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Page 11 of 21
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28
The Frostburg-Truth bus travels from Frostburg Mall through the City Center to Sojourner
Truth Park. The mall is 3 miles west and 2 miles south of the City Center. Truth Park is 4
miles east and 5 miles north of the Center. How far is it from Truth Park to the Mall to the
nearest tenth of a mile?
A
B
C
D
29
Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to
Seaside?
A
B
C
D
30
9.9 miles
3.6 miles
3.2 miles
6.4 miles
about 10 miles
about 50 miles
about 8 miles
about 40 miles
Find the coordinates of the midpoint of the segment whose endpoints are H(8, 2) and K(6,
10).
A
B
C
D
(7, 6)
(1, 4)
(14, 12)
(2, 8)
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Page 12 of 21
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31
M(9, 8) is the midpoint of the following:
The coordinates of S are (10, 10). What are the coordinates of R?
A
B
C
D
32
(9.5, 9)
(11, 12)
(18, 16)
(8, 6)
M is the midpoint of the segment:
Use the coordinates C(3, 4) and F(9, 8) to find the length below.
A
B
C
D
33
26
13
Find the perimeter of the triangle with vertices A(–5, –2), B(–2, –2), and C(–5, 2).
A
B
C
D
12 units
7 units
32 units
14 units
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Page 13 of 21
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34
What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
A
B
C
D
35
If a point is in the first quadrant, then its coordinates are positive.
If a point is not in the first quadrant, then the coordinates of the point are not
positive.
If the coordinates of a point are positive, then the point is in the first quadrant.
If the coordinates of a point are not positive, then the point is not in the first
quadrant.
Which expression models the area of the shaded region in the figure below?
A
B
C
D
36
Find, to the nearest tenth, the area of the region that is inside the square and outside the
circle. The circle has diameter 14 inches.
A
B
C
D
42.1
10.5
153.9
196
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Page 14 of 21
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37
What is the graph of the equation?
A
B
C
D
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Page 15 of 21
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38
For which situation could you prove the following using the HL Theorem only?
A
B
C
D
39
I only
II only
II and III
III only
Is there enough information to conclude that the two triangles are congruent? If so, what is
a correct congruence statement?
A
B
C
D
Yes;
.
Yes;
.
Yes;
.
No, the triangles cannot be proven congruent.
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Page 16 of 21
Midterm
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40
What is the second largest of the four angles named in the figure if the side included by
angles 1 and 2 is 11 cm, the side included by angles 2 and 3 is 16 cm, and the side
included by angles 3 and 1 is 14 cm?
A
B
C
D
41
Three security cameras were mounted at the corners of a triangular parking lot. Camera 1
was 158 ft from Camera 2, which was 121 ft from Camera 3. Cameras 1 and 3 were 140 ft
apart. Which camera had to cover the greatest angle?
A
B
C
D
42
Camera 2
Camera 1
cannot tell
Camera 3
Which list shows the sides in order from shortest to longest? The diagram is not to scale.
A
B
C
D
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Page 17 of 21
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43
Which three lengths could be the lengths of the sides of a triangle?
A
B
C
D
44
Two sides of a triangle have lengths 10 and 18. Which inequalities describe the possible
lengths for the third side x?
A
B
C
D
45
12 cm, 5 cm, 17 cm
10 cm, 15 cm, 24 cm
9 cm, 22 cm, 11 cm
21 cm, 7 cm, 6 cm
x > 8 and x < 28
x > 10 and x < 18
Use the information in the diagram to determine the height of the tree.
A
B
C
D
75 ft
150 ft
35.5 ft
37.5 ft
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Page 18 of 21
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46
Find the value of x.
A
B
C
D
47
4
8
6
DF bisects angle EDG. Find the value of x.
A
B
C
D
48
90
30
6
Find the center of the circle that you can circumscribe about a triangle with vertices E(4, 4),
F(4, 2), and G(8, 2).
A
B
C
D
(6, 3)
(4, 2)
(4, 4)
(3, 6)
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Page 19 of 21
Midterm
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49
Supply the missing reasons to complete the proof.
Given:
Prove:
A
B
C
D
ASA; Substitution
SAS; CPCTC
AAS; CPCTC
ASA; CPCTC
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Page 20 of 21
Midterm
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50
For a triangle, list the respective names of the points of concurrency of
• perpendicular bisectors of the sides
• bisectors of the angles
• medians
• lines containing the altitudes.
A
B
C
D
incenter
circumcenter
centroid
orthocenter
circumcenter
incenter
centroid
orthocenter
circumcenter
incenter
orthocenter
centroid
incenter
circumcenter
orthocenter
centroid
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Page 21 of 21