Geometry Advanced Practice Midterm
Study Guide January 2011
Name:
1. Draw and label for the situation described:
AB and CD intersect at point E.
2. Name the line and plane shown in the diagram. Use three points contained by the plane to identify the plane.
M
H
I
N
3. True or False:
ME and BE are opposite rays.
4. If XY = 33, what is the measure of XZ?
X
Z
Y
2x + 2
5x + 3
3x - 1
7x - 9
5. What is a postulate?
6. Which point is contained in the plane STU?
[A] Z
[B] V
[C] X
[D] W
7. Which segment is NOT parallel to AC?
[A] BD
[B] EG
[C] CD
[D] FH
8. Find the length of the segment joining points with coordinates -44 and 40.
9. Find the length of the segment joining points with coordinates -8 and 10.
10. Let D be between E and F. Use the Segment Addition Postulate to solve for r.
ED: 6r + 12
DF: 4r + 18
EF: 40
11. Which one of following is an acute angle?
[A]
[B]
[C]
12. The complement of an angle measures 30°. What is the measure of the angle?
[D]
13. The measure of <1 is 65°. What is the measure of <M?
M 1
14. Which of the following are not collinear?
[A] A, I, D
[B] B, J, C
[C] A, D, H
[D] F, K, G
u
v
15. If u and v are both perpendicular to line t, which is the relationship
t
between u and v?
[A] Lines u and v are not parallel.
[B] Lines u and v are perpendicular.
[C] Lines u and v are parallel.
16. If the bisector of
intersects at point R, and
[D] not enough information
is 11 cm, what is
?
17. Write a rule to describe a reflection over the x-axis
18. What is the image of the point (1, –4) after a rotation 270° clockwise about the origin?
19. Name the translation image of ΔOPQ after a reflection over line r and then a reflection over line t.
20. Which statement’s converse is true?
[A] If it Saturday, then it is a weekend.
[B] If it is January 1st, then it is the first day of the year.
[C] If it is an apple, then it is red.
[D] If it is ravioli, then it is pasta.
21. Which is the converse of this conditional: If I see it, then I eat it.
22. Write the converse of this statement: If x – 3 = 15, then x = 18. Is it true?
23. Supplementary angles are two angles whose measures have sum _____. Complementary angles are two angles
whose measures have sum _____.
24. Show this conditional statement is false by giving one counterexample: Odd integers less than 10 are prime.
25. Find the value of “y.”
6y + 10
6y - 10
26. Select the appropriate property of equality for the statement. If a = b, then a + c = b + c.
27. Select the appropriate property of equality for the statement. If a = b, then b = a.
28. Name the property: If a = b, and b = a, then a = c.
29. What is the classification for a polygon with 5 sides?
30. What is the classification for a polygon with 9 sides?
31. A graphic artist was painting a logo in the shape of a convex regular polygon. She measured one of the central
angles to be 72°. What is the name of the polygon she was painting?
W
32. Complete the proof.
Z
Given: WJ ≅ KZ, ∠W & ∠K are right angles.
Prove:  JWZ ≅  ZKJ
J
K
33. Select the geometric figure that possesses all of the following characteristics:
i. quadrilateral
ii. All sides same length
iii. two pair of parallel sides
[A] trapezoid
[B] parallelogram
[C] rectangle
34. Which of these descriptions does not guarantee that a figure is a rhombus?
[D] rhombus
[A] a parallelogram with perpendicular diagonals
[B] a quadrilateral with diagonals that both bisect opposite angles
[C] a parallelogram with a pair of adjacent sides congruent
[D] a polygon with all sides congruent
35. Exactly two sides of a certain quadrilateral are parallel. Which of the following best describes the
quadrilateral?
[A] rhombus
[B] rectangle
[C] trapezoid
[D] parallelogram
[C] r //q
[D] none of these
36. If <1 = <2, what must be true?
[A] p //q
[B] r //p
37. Which lines, if any, must be parallel based on the given diagram and information? Give the justification for the
conclusion.
b
a
Given: <1  <7
c
1
3 4
2
d
6 5
8 9
7
38. Find the measure of the third angle. The diagram is NOT to scale.
46
28
39. Find the number of sides of a polygon if the measures of its interior angles have a sum of
7,740°.
40. How many sides does a regular polygon have if each exterior angle measures 40?
41. Make sure you know the definitions of: equiangular, equilateral, regular polygon, concave, convex
42. Identify the concave polygon.
[A]
[B]
[C]
[D]
43. Find the value of the variable. The diagram is NOT to scale.
95
60
44. A Boy Scout club was doing a craft with paper cut out in the shape of a convex regular polygon. If one of
the interior angles has a measure of 140°, what is the name of the polygon?
C
45. If B is the midpoint of AC, D is the midpoint of CE, and BD =18, find AE.
B
D
A
E
46. Which statement is true?
[A] All rhombuses are squares.
[C] All quadrilaterals are rectangles.
[B] All quadrilaterals are squares.
[D] All rhombuses are quadrilaterals.
47. In the figure, EF is the midsegment of trapezoid ABCD. Find “x.”
B
x+1
3X - 1
C
x+4
E
4X + 3
F
2x + 2
A
48. <A and <B are supplementary and vertical. What is m<B?
[A] 45
[B] 90
[C] 135
6X - 4
D
[D] 180
49. The measure of an angle is 10 less than twice the measure of its supplement. What is the measure of the
angle?
50. What is the midpoint of the segment with endpoints (3, 5) and (7, -9)?
51. Classify <3 and <4 in the figure.
52. Quadrilateral ABCD  QRST. Which segment is congruent to BC?
53. By which postulate or theorem are the triangles congruent?
54. Which condition(s) will allow you to prove that l // m?
I. <1  <4
II. <2  <5
III. <3  <4
IV. m<2  <3
55. IF m< JCK = 81 and m<JCP = 120, what is the m<KCP?
1
l
2 3
4 5
J
m
K
P
C
56. Which angles form an adjacent pair?
4
1
2
3
[A] <1 & <3
[B] <3 & <4
[C] <2 & <3
[D] <2 & <4
57. Which best describes the relationship between the line that passes through (3, 3) & (1, -4) and the line that
passes through (1, 5) & (-2, -4)?
58. A line l, has slope -4/3. Determine whether the line through (-2, 3) and (6, -3) is a) parallel or b) perpendicular
to line l ?
59. Refer to the figure. Give a congruence statement for two triangles in the figure and name the theorem or
postulate that proves the congruence. IK  JH, HI  KJ I
J
K
H
[A]  HJK   KIH, by ASA
[C]  HJK   KIH, by SAS
[B]  HJK   KIH, by SSS
[D] none of these
B
60.  ADB   CDB by which theorem or postulate?
D
A
[A] SSS
C
[B] SAS
[C] ASA
61. Which one is NOT a valid test for triangle congruence? SSS, AAS, SAS, SSA?
62.
 ABD   CBD. Name the postulate or theorem that justifies the congruence.
A
D
B
[A] HL
[B] SAS
[C] ASA
E
[D] AAS
C
63. Use the information in the figure below to find m<D.
102
D
111
F
64. Could these be the sides of a triangle: 2, 2, 6?
65. A = (2, 5) and B = (-2, 3). Find the slope of AB.
66. AB has endpoints A = (-2, 5) and B = (-3, 1). CD has endpoints C = (1, 2) and D = (0, -2). What is the
relationship between AB and CD?
67. If three_____of one triangle are congruent to three_____of another triangle, then the triangles are
congruent.
[A] angles
[B] sides
[C] angle bisectors
[D] altitudes
H
68. Given AC // DF and m<EBC = 130º, find the m<BED.
A
B
D
A
E
125
F
F
G
E
69. Which angle is congruent to <FBA?
C
G
B
C
D
70. In quadrilateral FGHI, m <F = x, m<G = 4x, m<H = 3x, and m<I = 2x. Find the value of “x.”
OPEN-ENDED SECTION #1-5
Show any work necessary for full credit.
1. Given: C is the midpoint of AD.
4x
A
STATEMENTS
2x + 12
C
D
REASONS
1. C is the midpoint of AD
2. AC = CD
3. 4x = 2x + 12
4. 2x = 12
5. x = 6
2. Find the value of “y”.
3. Find the value of “x.”
3x 3y
+ 35
+ 20
5y4x- 16
3x++131 2x7x- 6+ 3
4x
4. Given: <N  <S, line l bisects TR at Q.
Prove:  NQT   SQR
STATEMENTS
line l
N
R
REASONS
Q
1. <N  <S
T
2. line l bisects TR at Q
3. TQ  RQ
4. <NQT  <SQR
5.  NQT   SQR
5. Find the value of “x”.
100
93
141
x+ 6
x
S