Download honors geometry—midterm exam—2006

HONORS GEOMETRY—MIDTERM EXAM—2006
CHAPTERS 1—6
NAME: _________________________ DATE: ________ PERIOD: ____
MULTIPLE CHOICE:
Q
R
# 1.
N
S
P
O
L
M
Determine which of the following is not shown in the figure above. __________
[A.]
[B.]
[C.]
[D.]
three lines that intersect in a point
two lines that do not intersect
three planes that intersect in a point
three planes that intersect in a line
T
# 2.
S
U1 2
43
5
P
6
Q
7
R
For the figure above, choose the false statement. _________
[A] US is a side of  2.
[C] Q is the vertex of  6.
# 3.
[B]
[D]
T
S
U1 2
43
P
5
6
Q
7
 2 is adjacent to  SUQ
 TUP is an obtuse angle.
Name a pair of adjacent angles in the figure.
________
R
[A]
[B]
[C]
[D]
 PQT and  SUQ
 1 and  4
 5 and  6
 6 and  TQR
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 2
T
# 4.
S
U1 2
43
P
5
6
Q
7
R
In the figure above, if US bisects  TUR, m  1 = 3 x + 18 and
m  TUR = 9 x – 6, find the value of x. ________
[A] x = 4
[B] x = 8
[C] x = 14
[D] x = 60
P
# 5.
M
L
N
Which of the following is the correct reason for Step 2 of the following proof? _
Given: In the figure above, MP bisects LN.
Prove: LM = ½ LN
STATEMENTS
REASONS
1. MP bisects LN.
1. Given
2. M is the midpoint of LN.
2. _________________
3. LM = ½ LN
3. Midpoint Theorem
(A.) Definition of segment bisector
(C.) Definition of midpoint
(B.) Midpoint Theorem
(D.) Segment Addition Postulate
# 6. Points K and L lie in plane P, and point N does not lie in plane P. What
is the intersection of plane P and the plane that contains points K, L, and N?
[A] KL
[B] KN
[C] LN
[D] The planes do not intersect.
# 7. In the figure, what is m  BJD? ___________
A
J
x
5x
C
D
B
[A] 30°
[B] 60°
[C] 100°
[D] 150°
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 3
P
104
# 8.
R
32
180
0
Q
In the diagram above, which number is paired with the bisector of  PQR?
______
[A] 36
[B] 52
[C] 68
[D] 78
# 9. Choose the true statement. _________
[A]
[B]
[C]
[D]
# 10.
Two acute angles are never complementary.
Two acute angles are never supplementary.
Vertical angles are never complementary.
Vertical angles are never supplementary.
L
V
1 2
3
4
5
N
P
T
R
In the figure above, if XP  LR, m  2 = 2 n – 4, and m  3 = n + 1, find the
value of n. ________________
[A] 5
[B] 29
[C] 31
[D] 61
# 11. Two lines are parallel if: _______________
[A] they do not intersect
[C] they are not skew
# 12.
[B] they are coplanar and do not intersect
[D] they are noncoplanar and do not intersect
x
(2 y)
[A]
[B]
[C]
[D]
60
In the figure above, find the values of x and y. _________
x = 90, y = 45
x = 90, y = 120
x = 90, y = 60
x = 120, y = 45
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 4
# 13. If two parallel lines are cut by a transversal, which one of the following is
not necessarily true? _________
[A]
[B]
[C]
[D]
# 14.
The corresponding angles are congruent.
The same-side interior angles are supplementary.
The corresponding angles are supplementary.
The alternate interior angles are congruent.
30
(2 x + y)
(3 x – y)
60
In the figure above, find the values of x and y. ________
[A] x = 54, y = 42
[C] x = 150, y = 120
# 15.
[B] x = 54, y = 48
[D] x = 132, y = 48
S
T
V
[A] VT
[C] VT
U
# 16.
B
A
C
D
O
E
Which of the following best describes what
 SVT and  TVU have in common?
[B] VT
[D] V, T
Which of the following is a pair of supplementary
angles? ____
F
[A]  BOF and  BOA
[C]  COF and  AOF
[B]  COD and  DOE
[D]  DOE and  DOB
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 5
# 17. What are the coordinates of the midpoint of EF? ___________
F (- 6, 10, 0)
[A] (- 2.5, 7, - 2.5)
[B] (- 3.5, 7, 2.5)
[C] (4.5, 3, - 2.5)
E (1, 4, - 5)
[D] (- 1.5, 3, 2.5)
# 18. Using the map below, the highway department locates two exits between
Tomstown and Mount Lookout. From Tomstown, Exit 1 is halfway to
Mount Lookout, and Exit 2 is three-fourths of the way to Mount Lookout.
Mount Lookout (78, 71)
Exit 2
Exit 1
Tomstown (2, 3)
What are the coordinates for Exit 2? _____
[A] (74, 37)
[C] (40, 37)
[B] (59, 54)
[D] (68, 54)
# 19. The county planning department designs a new park in the shape of a
parallelogram. They put in two diagonal walkways. What will be the
coordinates of the intersection of the diagonal walkways? ________
(12, 11)
(0, 10)
(12, 3)
(0, 2)
[A] (6, 6.5)
[B] (5, 6.5)
[C] (5.5, 6)
[D] (6, 2.5)
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 6
# 20. Given: m  1 = 4 x, m  2 = (3 x + 10), and m  3 = (2 x + 17)
What is m  2? __________
3
[A] 61
1
[B] 47
[C] 31
[D] 17
2
# 21. If ABCD is a rhombus and m  ABC = 100, what is the measure of  1?
________
A
B
[A] 40
[B] 50
[C] 80
[D] 90
1
D
C
# 22. ABCD is a parallelogram. If m  BCD = (6 x + 20) and
m  DAB = (2 x + 80), what is the value of x? ________
[A] 8.3
[B] 12.5
[C] 15
M
# 23.
N
Which of the following statements is true about
this picture? ______
12
8
14
[A] m  O > m  M
[C] m  M < m  N
[D] 25
O
[B] m  M > m  N
[D] m  N < m  O
# 24. Write the following statement in “if-then” form. ______
“Two angles that form a linear pair are supplementary.”
[A]
[B]
[C]
[D]
If
If
If
If
two angles are supplementary, then they form a linear pair.
two angles form a linear pair, then they are supplementary.
two angles are not supplementary, then they form a linear pair.
two angles do not form a linear pair, then they are supplementary.
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 7
# 25. What is the inverse of the statement below? _______
If a triangle is scalene, then no two angles are congruent.
[A]
[B]
[C]
[D]
If the triangle is not scalene, then there are two congruent angles.
If two angles of a triangle are congruent, then the triangle is scalene.
If there are two congruent angles in a triangle, then the triangle is not scalene.
If the triangle is not scalene, then there are no congruent angles.
# 26. If k | | m | | n, which of the statements justifies the conclusion that
 1   2   3?
[A] If k | | m | | n with transversal t, then alternate
interior angles are congruent.
n
3
m
[B] If k | | m | | n with transversal t, then vertical
angles are congruent.
2
k
1
[C] If k | | m | | n with transversal t, then alternate
exterior angles are congruent.
t
[D] If k | | m | | n with transversal t, then
corresponding angles are congruent.
# 27.
40
y
x
60
In the drawing, what is the measure of angle y? _______
[A] 40
[B] 60
[C] 80
[D] 100
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 8
# 28. A rectangular card is cut along AB and BC as shown below. What is the
area of  ABC? _____
[A] 5.83 in. 2
[B] 7.5 in. 2
[C] 8 in. 2
[D] 15 in. 2
# 29. If m  1 = 35,  1 and  2 are complementary, m  2 = m  3, and
m  3 = m  4, what is m  4? _________
[A] 35
[B] 55
[C] 90
[D] 145
# 30. What can you conclude if you know m  P + m  Q = m  R + m  Q?
____
[A] m  P = m  Q
[C] m  Q = m  R
[B] m  P = m  R
[D]  P and  R are supplementary.
# 30. Point Q is the midpoint of PR. PQ = 2 x + 1 and QR = 3 x – 6. What is
PR? ____
[A] 7
[B] 14
[C] 15
[D] 30
# 31.  AXB and  BXC are adjacent, complementary angles, and  BXC
and  CXD are adjacent, supplementary angles. Which statement is true?
____
[A]
[B]
[C]
[D]
 AXB
 AXB
 CXD
 DXA
and
and
and
and
 BXC
 CXD
 DXA
 AXB
are vertical angles.
are vertical angles.
are supplementary.
are supplementary.
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 9
# 32. What do you need to know to conclude that m  1 = m  4? _________
c
a
1
2
3
4
b
[A] Line a is parallel to line b.
[B] Line a is parallel to line c.
[C] Line a is perpendicular to line c.
[D] Line b is perpendicular to line c.
# 33. Lines j, k, m, and n lie in a plane. You know line j is perpendicular to
line n, m is perpendicular to line n, and line k is parallel to line m. What
can you conclude?
[A] Line n is parallel to line k.
[B] Line j is perpendicular to line m.
[C] Line k is perpendicular to line j. [D] Line j is parallel to line k.
# 34. If m  F = 60, what is m  FKL? _________
G
K
F
[A] 30
[B] 60
[C] 120
[D] 150
L
H
# 35. Which of the following is an equation of a line parallel to the line with the
equation 3 y = - 5/2 x + 4? ____
[A] y = - 5/2 x + 7
[C] y = - 5/6 x + 7
[B] 3 y = - 2/5 x + 4
[D] 4 y = - 5/6 x + 3
# 36. Which of the following is an equation of a line parallel to the one shown?
y
_______
3
[A] 2 x – 2 y = 3 [B] – 3 x + y = 2
2
(1, 2)
1
[C] x – y = - 3
(2, 0)
0
1
2
3
x
[D] – 2 x – y = - 9
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 10
# 37. Which of the following is an equation of a line perpendicular to the line with
equation 2 y = - x + 2/3 ? _________
[B] y = 2 x – 6
[D] 6 y = 3 x + 2
[A] 2 y = x + 2/3
[C] y = x – 3
# 38. In the figure, what is the value of x? __________
70
50
x
[A] 170
[B] 140
[C] 120
[D] 110
# 39. In the figure below, C is the midpoint of BE, m  B = m  E, and
AB = DE. What is the measure of  ACB?
A
D
80
B
[A] 40
[B] 50
[C] 80
[D] 100
E
# 40. In the figure below,  K   M. What is the length of NK? ________
K
[A] 65
[B] 51
[C] 21
[D] 16
(4 x + 1)
N
(3 x + 17)
M
# 41. In the figure below, P is the centroid of  DEF, and PG = 4.
E
What is EG? _____
[A] 8
[B] 12
H
P
K
[C] 16
4
G
G
F [D] EG cannot be determined
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 11
# 42. A triangle has a perimeter of 24 inches. What is the perimeter of the
triangle formed by its midsegments? _____
[A] 6 in.
[B] 8 in.
[C] 12 in. [D] 24 in.
# 43.  ABC and  CBD are adjacent angles, m  ABC = 60,
and m  CBD = 50. Also, BA = BC = BD.
Which statement is true? _________
D
C
50
60
B
A
[A] AC  AB
[B] AC  BD
[C] AC  CD
[D] AC  DA
# 44. A quadrilateral has interior angles with measures x , 2 x , 3 x , and
4 x . What is the value of x? _____
[A] 40
[B] 36
[C] 20
[D] 18
# 45. In parallelogram QRST, QS = 4 y – 3 and RT = 2 y + 6, and
RT = 2 (QS). What is QS? ______
[A] 2
[B] 5
[C] 10
[D] 12
# 46. In the figure, RHMB is a rhombus. What is m  B? ________
H
R
61 M
[A] 151
[B] 122
[C] 119
[D] 110
B
# 47. Quadrilateral KITE is a kite. If m  KTI = 22, what is m  ITE?
K
______
I
[A] 22
[B] 44
[C] 48
E
T
[D] 66
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 12
# 48. UVWX is a trapezoid with midsegment YZ. What is the length of UV?
_______
U
k
Y
X
V
Z
39
[A] 25
[B] 20
[C] 19
[D] 12
W
3k–2
# 49. A rhombus has diagonals of length 20 centimeters and 40 centimeters.
What is the area of the rhombus? ___
[A] 800 cm 2
[B] 600 cm 2
[C] 400 cm 2
[D] More information is needed to determine the area
# 50. Suppose  JKL   QRS. Which statement can you conclude? ________
[A]  L   Q
[C]  Q   S
[B] JK = SR
[D] JL = QS
# 51. In  DEF, m  F  m  D  m  E. Which of the following is true?
__________
[A] DE  EF and EF  DF
[C] DE  EF and DF  EF
[B] EF  DE and EF  DF
[D] EF  DE and EF  DF
# 52. For which type of convex polygon is the sum of the interior angles equal to
the sum of the exterior angles, one at each vertex? _______
[A] triangle
[B] hexagon
[C] pentagon
[D] quadrilateral
# 53. If m  P = 120, what is the sum of the measures of the remaining interior
angles? ___
Q
R
[A] 240
[B] 360
S
P 120
U
T
[C] 600
[D] 720
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 13
# 54. The measure of each exterior angle of a regular polygon is 45. How many
sides does the polygon have? ____
[A] 4
[B] 5
[C] 8
[D] 9
# 55. Triangle MNO has coordinates M (0, 2), N (1, 0), and O (5, 1). What
type of triangle is  MNO? ______
[A] isosceles
[B] right
[C] scalene
[D] equilateral
# 56. In triangle XYZ, W is between Y and Z. The coordinates are X (2, 3),
Y (5, 0), Z (0, 0), and W (2, 0). What is XW? ______
[A] altitude
[B] median
[D] perpendicular bisector of a side
[C] angle bisector
# 57. What is the most specific name for quadrilateral ABCD with vertices
A(0, 0), B (3, 4), C (6, 0), and D (3, - 4)? ________
[A] parallelogram
[B] rectangle
[C] rhombus
[D] trapezoid
# 58. In rectangle ABCD, diagonal AC = (3 x – 9) and diagonal BD = (x + 13).
What is AC? ________
[A] 16
[B] 18
[C] 24
[D] 32
# 59. In parallelogram RSTU, the diagonals intersect at E. If RE = 10 and
SU = 16, what is RT? _____
[A] 20
[B] 16
# 60.
A
[D] 8
 ABC is an isosceles triangle with AB = BC and
median BD. The perimeter of  ABC is 60 units.
What is AB? ________
B
10
[C] 10
D
C
[A] 10 units
[B] 15 units
[C] 20 units
[D] 40 units
HONORS GEOMETRY—MIDTERM EXAM—2006—PAGE 14
# 62. A triangle has interior angles that measure 3 x, (2 x + 15), and (x + 45).
What is the measure of the largest exterior angle? ________
[A] 160
[B] 125
[C] 120
[D] 115
# 63. Joe is building a room. What do the planes of the floor and the back wall of
the room most closely represent? ______
[A] coplanar planes
[C] parallel planes
[B] intersecting planes
[D] bisecting planes
# 64. Jane drew two triangles and labeled them to show specific sides and angles
were congruent. Given her diagram below, what reason can Jane use to
show that the triangles are congruent? ______
[A] Angle-Angle-Angle (AAA)
[C] Angle-Angle-Side (AAS)
[B] Angle-Side-Angle (ASA)
[D] Side-Angle-Side (SAS)