Download Geo Fundies MT Revie..

Geometry Fundamentals Midterm Exam Review Name: _______________________
(Chapter 1, 2, 3, 4, 7, 12)
Date: _________ Mod: _________
Use the figure at the right for #1-4
1. What is another name for plane P?
A. plane AE
B. plane A
C. plane BAD
D. plane BAC
2. Which segment is on line n?
A. AD
B. BC
C. AD
D. BE
3. Which is the name of a ray with endpoint A?
A. DA
B. BC
C. CA
D. AB
4. Name the intersection of plane P and line m?
A. line n
B. point A
C. AC
D. AE
5. What is the measure of RT ?
A. 5
B. 16
C. 26
D. 40
Use the figure at the right for #6-7
6. Which term describes  PMQ?
A. obtuse
B. straight
C. right
D. acute
7. What is m  PMN?
A. 22°
B. 90°
C. 68°
D. 112°
8. AB bisects  CAD. Find x.
A. 2
B. 6
C. 4
D. 8
9. X is the midpoint of WY . Find WX.
A. 1
B. 6
C. 4
D. 12
10. Two angles are supplementary. If m  1 = 67°, what is m  2?
11. Find the measure of the complement of  T, where m  T = 49.3°.
12. Reflect the figure with the given vertices across x-axis. A(-4, 1), B (2, 4), C (3, -2)
A’ _____ B’ _____ C’ _____
13. Translate the figure with the given vertices along the vector <2, 3>. A (-2, 1),
B (4, 3), C (2, -2)
A’ _____ B’ _____ C’ _____
14. Rotate the figure with the given vertices about the origin with a
counterclockwise 90˚ angle of rotation.
A (2, 3), B (-2, 1), C (1, -1)
A’ _____ B’ _____ C’ _____
15. Does the figure have line symmetry? ______ If yes, draw all lines.
Does the figure have rotational symmetry? _____ If yes, give the angle of
rotation and order of symmetry.
Angle _____ Order _____
16. Given GH with endpoints G (-11, 4) and H (-1, -9), what are the coordinates of the
midpoint of GH ?
A. (-12, -5)
B. (-6, -2.5)
C. (-10, 13)
D. (-5, 6.5)
17. M is the midpoint of RS . R has coordinates (-12, 4) and M has coordinates (1, -2).
What are the coordinates of S?
A. (-5.5, -1)
B. (-11, 2)
C. (13, 6)
D. (14, -8)
18. What is the distance from M (-1, 6) to N (11, 1)?
A. 12 units
B. 149 units
C. 13 units
D. 169 units
19. What is the distance from V to W?
A. 17 cm
B. 23 cm
C. 120 cm
D. 289 cm
20. What transformation is shown?
A. rotation
B. reflection
C. translation
D. image
21. Given a point in the coordinate plane, the rule (x, y)  (x + 2, y - 3) translates the
point in which direction?
A. 2 units to the left and 3 units up
B. 3 units to the left and 2 units down
C. 3 units right and 2 units up
D. 2 units to the right and 3 units down
22. Which is the biconditional statement of the conditional statement
“If x3 = -1, then x = -1”?
A. If x = -1, then x3 = -1
B. x3 = -1 if x = -1
C. x3 = -1 if and only if x = -1
D. x = -1  x3 = -1
23. For which statement is the converse false?
A. If Mary can swim, then she can swim the crawl.
B. If it is raining outside, then the temperature is above freezing.
C. If Greg has two children, then he has one son and one daughter.
D. If Caroline can stand up, then she can walk.
24. Which is a counterexample of the statement?
If an animal has wings, then it can fly.
A. penguin
B. robin
C. duck
D. rabbit
25. Write a conditional statement of the biconditional statement
“An angle is an acute angle if and only if the angle’s measure is less than 90˚.
26. Fill in the reasons.
5 = 2 – ½x
Given
2 – ½x = 5
______________
2(2- ½x) = 10
______________
4 – x = 10
______________
-x = 6
______________
x = -6
______________
27. Given: BD bisects  ABC
Prove: BG bisects  FBH
Statements
Reasons
1. BD bis.  ABC
1. _________________________
2. m  1 = m  2
2. _________________________
3. m  1 = m  4
3. _________________________
4. m  4 = m  2
4. _________________________
5. m  2 = m  3
5. _________________________
6. m  4 = m  3
6. _________________________
7. BG bisects  FBH
7. _________________________
Use the figure at the right for #28-29
28. Classify EH and DH
A. skew
B. parallel
29. How many segments are skew to AE ?
A. 1
B. 2
C. perpendicular
D. none of these
C. 3
D. 4
C.  3 &  6
D.  6 &  7
Use the figure at the right for #30-31
30. Which are alternate interior angles?
A.  1 &  3
B.  1 &  8
31. Which statement is true?
A.  1 and  2 are alternate interior angles.
B.  1 and  3 are corresponding angles.
C.  3 and  6 are alternate exterior angles.
D.  3 and  7 are same-side interior angles.
32. Which correctly completes the sentence?
If two parallel lines are cut by a transversal, then the two pairs of same-side
interior angles are _____________________.
A. supplementary
B. complementary C. corresponding D. congruent
33. What type of angle is  1?
A. acute
B. right
C. obtuse
D. straight
34. Given RS || QP , what is the value of x?
A.
B.
C.
D.
6
9
72
108
Use the figure at the right for #35-36
35. Which information proves that r || s?
A.  1   3
B.  4   5
C.  4   6
D.  5   6
36. If m  3 = (4x + 20)° and m  5 = (6x + 10)°, what value of x proves that r || s?
A. 5
B. 15
C. 40
D. 100
37. If a transversal is perpendicular to one of two parallel lines, how many different
angle measures are formed?
A. 1
B. 3
C. 4
D. 8
38. Which is a possible value of x?
A. -2
B. 1
C. 3
D. 4
39. Which describes the slope of a horizontal line?
A. positive
B. negative
C. zero
40. What is the slope of a line through (-1, 4) and (5, 2)?
1
A. -3
B. –½
C. 3
D. undefined
D.
3
2
41. Given A (1, 5), B (-2, -1), C (1, 1) and D (3, 5), what type of lines are AB and CD ?
A. parallel
B. perpendicular C. horizontal
D. vertical
42. Which is the equation of the line through (1, 11) and (-2, 2)?
1
A. y = 3x - 8
B. y = x + 8
C. 3x + y = 8
3
D. -3x + y = 8
43. Classify the triangle.
A. isosceles acute
B. isosceles obtuse
C. scalene acute
D. scalene obtuse
44. What is m  KLM?
A. 3°
B. 22°
C. 42°
D. 64°
45. What is the m  U?
A. 5°
B. 15°
C. 40°
D. 120°
46. Two congruent triangles have the following corresponding parts: RS  UV , RT 
UW , and  R   U. Which is NOT necessarily a correct congruence statement?
A. ∆RST  ∆UVW
B. ∆STR  ∆VWU C. ∆TRS  ∆VWU D. ∆TRS  ∆WUV
47. ∆KLM  ∆RST, m  L = (3x + 15)° and m  S = (6x + 3)°. What is the value of x?
A. 2
B. 4
C. 6
D. 27
Use the figure at the right for #48-49
48. If AD = 5y + 7 and BC = 7y - 3, what must the
value of y be to prove ∆AED  ∆CEB by the SSS postulate?
A. 2
B. 5
C. 17
D. 32
49. What postulate or theorem justifies the congruence statement ∆ABE  ∆CDE?
A. SSS
B. ASA
C. SAS
D. AAS
50. What method proves the triangles are congruent?
A. SSS
B. SAS
C. HL
D. AAS
51. For these triangles, select the triangle congruence statement and the postulate or
theorem that supports it.
A.  ABC   DEC; SAS
B.  ABC   DEC; AAS
C.  BAC   CED; AAS
D.  BAC   CED; SSS
52. Find CA.
53. Find a, b, and c.
54. What is the value of x?
A. 12
B. 19.5
C. 18
D. 60
Use the partially completed proof for #55-57
Given: l || m,  1   3
Prove: r || p
Statements
Reasons
1. l || m
1. Given
2.  1   2
3.  1   3
2. Corresponding angles
postulate
3. ________________
4.  2   3
4. ________________
5. r || p
5. ________________
55. Which reason belongs in step 3?
A. transitive property of congruence
B. given
C. corresponding angle postulate
D. converse of alternate exterior angle theorem
56. Which reason belongs in step 4?
A. transitive property of congruence
B. given
C. corresponding angle postulate
D. converse of alternate exterior angle theorem
57. Which reason belongs in step 5?
A. transitive property of congruence
B. given
C. corresponding angle postulate
D. converse of alternate exterior angle theorem
58. Find x
59. Find m  A.
60. Find x.
61. The ratio of the side lengths of a triangle is 3 : 4 : 5. What could NOT be the
side lengths of the triangle?
A. 1.5 in., 2 in., 2.5 in.
B. 4.5 in., 6 in., 7.5 in.
C. 7.5 in., 10.5 in., 12.5 in.
D. 8.25 in., 11 in., 13.75 in.
62. What is the value of x?
A.  81
x  3 2x  4

12
8
B. 9
C. 4.5
D. Not here
63. If 21x = 63y, what is the ratio of x to y expressed in simplest form?
1
3
3
21
A.
B.
C.
D.
3
9
1
7
64. The ratio of a dog park’s length to its width is 11 : 9. If the width of the field is
180 yards, what is the length of the field? If necessary, round to the nearest whole
number.
A. 147 feet
B. 220 feet
C. 1620 feet
D. not here
65. Which similarity statement is true for rectangles JKLM and PQRS given that
JK = 6, JM = 5, QR = 15, and PQ = 12.5?
A. rectangle JKLM ~ rectangle PQRS
B. rectangle JKLM ~ rectangle QRSP
C. rectangle JKLM ~ rectangle RQPS
D. rectangle JKLM ~ rectangle SRQP
66.  JKL ~  MNO. The similarity ratio of  JKL to  MNO
is 5 : 2. What is the length of MN?
A. 6
B. 10.8
C. 14
D. 37.5
67. Which similarity postulate or theorem lets you conclude that  ABC ~  CDE?
A. AA
B. SAS
C. SSS
D. Triangles are not similar
68. What is ST?
A. 18.75
B. 20
C. 32.5
D. 45
69. What information guarantees that XY || AC ?
A. XB = 20, BY = 25
B. XB = 24, BY = 30
C. XB = 25, BY = 20
D. XB = 32, BY = 40
70. In  JKL, the bisector of  J divides KL into XK with length (y + 3) and XL with
length (2y). If JK = 12 and JL = 16, which could be the length of XK ?
A. 6
B. 9
C. 12
D. 16
71. A student who is 60 inches tall measured shadows to find the height of a tree.
The student’s shadow was 24 inches long and the shadow of the tree was 13 feet long.
Which proportion should the student use to find the height of the tree in inches?
60 24
5 2
60 x
60
x
A.
B.
C.
D.




156
x
13 x
24 13
24 156
72. A blueprint uses a scale of 1.5 in. : 24 ft. If the actual room has a width of 12
yards and a length of 17 yards, how long is the room in blueprint?
1
3
3
1
A.
B. 1 in.
C. 2 in.
D. 3 in.
in.
16
16
4
4
73. Verify  PQR and  PRS are similar.
74. Verify  JKL and  JMN are similar.
75. Find EF to the nearest tenth.
76. Find x.
77. Which is NOT a correct classification for the triangle?
A. acute
B. isosceles
C. equiangular
D. scalene
78. What is the length of side BC ?
A. 8
B. 6
C. 10
D. 24
79. Given the perimeter of  ABC = 12 feet, find perimeter of  XYZ.
80. Given the area of  ABC = 6 feet2, find the area of  XYZ.
Geometry Fundamentals Midterm Exam Review Name: _______________________
(Chapter 1, 2, 3, 4, 7, 12)
Date: _________ Mod: _________
Vocabulary - Matching
Match each vocabulary term with its definition.
A. ray
D. complementary angles
G. acute angle
J. supplementary angles
M. perpendicular lines
P. equilateral triangle
S. equiangular triangle
V. similar polygons
Y. proportion
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
B. coplanar
E. biconditional
H. postulate
K. linear pair
N. skew lines
Q. slope
T. scale factor
W. reflexive prop.
C. segment bisector
F. congruent angles
I. obtuse angle
L. parallel lines
O. theorem
R. isosceles triangle
U. CPCTC
X. transitive prop.
1. points that lie in the same plane
2. a statement that is accepted without proof, an axiom
3. a part of a line that starts at an endpoint and extends forever in one direction
4. a segment, ray, or line which divides a segment into two congruent parts
5. angles that have the same measure
6. an angle that measures greater than 0˚ and less than 90˚
7. an angle that measures greater than 90˚ and less than 180˚
8. two angles whose measures have a sum of 180˚
9. a pair of adjacent angles whose noncommon sides are opposite rays which
form a line
10. a statement that can be written in the form “p if and only if q”
11. two angles whose measures have a sum of 90˚
12. lines that do not intersect and are not in the same plane
13. lines in the same plane that do not intersect
14. lines that intersect at 90˚ angles
15. a statement that has been proven
16. the measure of the steepness of a line
17. a triangle with three congruent sides
18. a triangle with at least two congruent sides
19. a triangle with three congruent angles
20. the ratio of two corresponding linear measurements in a pair of similar figures
21. an equation that states two ratios are equal
22. two polygons whose corresponding angles are congruent and whose
corresponding sides are proportional
23. AB = AB and m  1 = m  1
24. if a = b and b = c, then a = c
25. an abbreviation for “corresponding parts of congruent triangles are congruent”
that is used as a reason in proof after two triangles are proven congruent
Geometry Fundamentals Midterm Exam Review Name: _______________________
(Chapter 1, 2, 3, 4, 7, 12)
Date: _________ Mod: _________
Extended Response
1. Neatly draw and label plane XYZ. Then draw MN intersecting the plane at point P.
2. Neatly draw and label plane XYZ. Then draw intersecting lines n and m contained in
the plane.
3. Given the conditional, write the converse and biconditional statement. Determine
the truth value of each.
The measure of a straight angle is equal to 180°. Truth value: _____
Converse: ________________________________________________________
_____________________________________________ Truth value: _____
Biconditional: _____________________________________________________
_____________________________________________ Truth value: _____
4. Why are the triangles similar? ______
Find PV. ________
5. Complete the proof.
Given :
M is the midpoint of PQ and RS
Prove:
QR  PS


Statements
Reasons