Geometry Midterm Review
Geometry Midterm Review Test
2010 – 2011
You must show your work to receive credit!
Ms. Vasili
A note to remember, for this exam: It is always helpful to draw a picture. I encourage you to do that
for any problem a picture is not given. GOOD LUCK.
Name:___________________
Date:_______________
Period:______
Choose the best answer for each question.
1. Find the length of the segment with endpoints L(-1, -3) and M(-6, 9).
A. 13 B. 17 C. 5 D. 12
2. Points A, B and D
A. determine a plane B. are collinear
C. are contained in only plane P D. are noncoplanar points
3. What is the intersection of planes P and R.
A points A, D and B B. [pic] C. [pic] D. [pic]
4. What is the measure of [pic] if R is between Q and T, QR = 14 and RT = 5?
A. 10 B. 11 C. 19 D. 9
5. Find the coordinates of the midpoint of the segment with endpoints D(6, 6) and E(-2, 2).
A. (3, 4) B. (2, 4) C. (4, 8) D. (1, -1)
6. What are the sides of [pic]?
A. [pic] B. [pic]
C. [pic] D. [pic]
7. [pic] and [pic] are
A. adjacent B. vertical C. supplementary D. complementary
8. [pic] and [pic] are
A. adjacent B. vertical C. supplementary D. complementary
9. [pic] and [pic] are
A. adjacent B. vertical C. complementary D. linear pair
10. [pic] and [pic] are
A. adjacent B. vertical C. linear pair D. complementary
11. Find [pic].
A. 25 B. 155
C. 175 D. 5
12. If [pic]and [pic], find [pic]
A. 150 B. 130
C. 70 D. 80
13. Find [pic]if [pic] bisects [pic], [pic] and [pic]
A. 48 B. 18
C. 9 D. 24
14. Choose the converse of “If [pic], then [pic] = [pic].
A. If [pic] = [pic], then [pic]
B. If [pic], then [pic]
C. If [pic] = [pic], then [pic] = [pic].
D. None of these
15. Identify the hypothesis of the statement “If today is Tuesday, then tomorrow is Wednesday.”
a. Today is not Tuesday
b. Today is Wednesday
c. Today is Tuesday
d. Tomorrow is Wednesday
16. Identify the if-then form of the following: All cars have four wheels.
a. If a vehicle has four wheels, then it is a car.
b. If a vehicle is a car, then it has four wheels.
c. If a vehicle is not a car, then it does not have four wheels.
d. None of these
17. Choose the statement that follows (1) and (2) by the law of detachment.
i. Right angles are congruent.
ii. [pic] and [pic] are right angles
A. m[pic] = 90 B. m[pic] = 90 C. [pic] D. [pic] = [pic]
18. Which statement represents the law of syllogism.
a. If [pic]is a true conditional and p is true, then q is true.
b. If [pic]and [pic]are true conditionals, then [pic]is true.
c. If a, b and c are real numbers, then a(b + c) = ab + ac.
d. None of these
19. The transitive property of equality states “If a = b and b = c, then _____ “.
A. b = a B. a = c C. c = b D. b = b
20. [pic] and [pic] form a linear pair and [pic] Find [pic]
A. 62 B. 28 C. 118 D. 90
21. Given [pic] and [pic]= 72, find [pic]. ( for 21-23, the rectangle represent parallel lines)
A. 108 B. 72
C. 18 D. 112
22. Given [pic], [pic]= 9x +5 and [pic]= x + 37, find the value of x.
A. 32 B. 4
C. 41 D. 39
23. Given [pic] and [pic] = 3x + 28, find the value of x so that [pic].
A. 26 B. 13
C. 67 D. 75
24. A right triangle must be
A. isosceles B. acute C. scalene D. either isosceles or scalene
25. Find the measures of the legs of an equilateral triangle PQR if PQ = 5x – 7 and PR = 2x + 5.
A. 39 B. 13 C. 12 D. 4
26. In triangle ABC, what is the angle opposite [pic]?
A. [pic] B. [pic] C. [pic] D. [pic]
27. In triangle DEF, if [pic] and [pic] is the hypotenuse, then triangle DEF is
A. acute and scalene B. right and scalene
C. right and isosceles D. obtuse and isosceles
28. The measures of two angles of a triangle are 38 and 47. What is the measure of the third angle?
A. 85 B. 95 C. 133 D. 142
29. If [pic], then [pic] is congruent to
A. [pic] B. [pic] C. [pic] D. [pic]
30. Which of the following is not a postulate used to prove the congruence of two triangles?
A. ASA B. SSA C. SAS D. SSS
31. The measure of the vertex angle of an isosceles triangle is 120. That is the measure of the base angle?
A. 60 B. 30 C. 35 D. 40
32. Name one additional pair of corresponding parts that need to be congruent in order to prove that
[pic] by ASA.
A. [pic] B. [pic]
C. [pic] D. [pic]
33. Identify the median of triangle ABC.
A. [pic] B. [pic]
C. [pic] D. [pic]
34. Identify the altitude of triangle ABC.
A. [pic] B [pic]
C. [pic] D. [pic]
35. In triangle ABC, if [pic] and [pic] is an angle bisector, find [pic]
A. 90 B. 51
C. 39 D. 12
36. What is the longest side of the figure QUAD.
A. [pic] B [pic]
C. [pic] D. [pic]
37. In triangle EFG, [pic]= 6x – 8, [pic]7x + 3, and [pic] = 3x – 7. Choose the list that shows the sides correctly ordered from shortest to longest.
A. [pic] B. [pic]
C. [pic] D. [pic]
38. Determine which set of numbers can be the measures of the sides of a triangle.
A. 13, 10, 16 B. 1, 2, 3 C. 5.2, 11, 4.9 D. 208, 9, 219
39. Two sides of a triangle have lengths 15 cm and 19 cm. Which measurement can be the length of the third side?
A. 6 cm B. 4 cm C. 40 cm D. 36 cm
40. If the sides of a triangle have measures 3x + 4, 6x – 1 and 8x + 2, find all possible values of x.
A. x > -1 B. [pic] C. [pic] D. x > 0
41. If M is the midpoint of [pic], [pic], JL = 10x + 2, and LK = 6x + 14, which is a possible value of x?
a. 1
b. 2
c. 3
d. 4
Properties
State the property, theorem, postulate or definition used to make the conclusion.
42. If UV = VW, then VW = UV. ___________________________________________________
43. If [pic]is a right angle, then [pic]is 90[pic]. _____________________________________________
44. 2(x – 50) = 2x – 100. __________________________________________
45. If [pic] and [pic]are vertical angles, then [pic]. ______________________ ___________________
46. If [pic], then [pic]is a right angle. _________________________
47. AB + BC = AC. __________________________________________
48. If [pic], then [pic]. ______________________________________________________
49. [pic]. ________________________________________________________________________
50. If 2x + 4 = 17, then 2x = 13. ____________________________________________________________
51. T is the midpoint of [pic], then [pic]. ________________________________________________
52. If [pic] and [pic], then [pic]. ________________________________________________
53. If [pic] and [pic]are a linear pair, then they are supplementary. _______________________________
54. If [pic] bisects [pic], then [pic]. ___________________________________________
55. If [pic] and [pic]are supplementary, then [pic]. _____________________________________
56. If [pic], then [pic]. _______________________________________________________
57. [pic], then [pic]. _____________________________________________________________
58. . Given: [pic] Prove: [pic] ( the symbol represent the triangle sign)
F is a midpoint of [pic]
Statements Reasons
1. ___________________________ 1._______________________________________________________
2. ___________________________ 2._______________________________________________________
3. ___________________________ 3._______________________________________________________
4. ___________________________ 4._______________________________________________________
5. ___________________________ 5._______________________________________________________
6. ___________________________ 6. ______________________________________________________
7. ____________________________ 7.________________________________________________________
59. Given: [pic] Prove: [pic]
[pic]
Statements Reasons
1. ____________________________ 1. _____________________________________________________
2. ____________________________ 2. _____________________________________________________
3. ____________________________ 3. _____________________________________________________
4. ____________________________ 4. ______________________________________________________
60. Given: W is a midpoint of [pic] Prove: [pic]
[pic]
Statements Reasons
1. ___________________________ 1. ______________________________________________________
2. ___________________________ 2. ______________________________________________________
3. ___________________________ 3. ______________________________________________________
4. ___________________________ 4. ______________________________________________________
5. ___________________________ 5. ______________________________________________________
6. ___________________________ 6. ______________________________________________________
7. ____________________________ 7._______________________________________________________
61. Given: 3(2x – 5) + 1 = 2(x – 3)
Prove: x = 2
Statements Reasons
1.___________________________ 1.__________________________________
2.___________________________ 2.__________________________________
3.___________________________ 3.__________________________________
4.___________________________ 4.__________________________________
5.___________________________ 5.__________________________________
6.___________________________ 6.__________________________________
62. Given: a (( b
(1 ( (4
Prove: c (( d
Statements Reasons
1. a (( b 1.__________________________________
2. (1 ( (3 2.__________________________________
3. (3 ( (1 3.__________________________________
4. (1 ( (4 4.__________________________________
5. (3 ( (4 5.__________________________________
6. c (( d 6.__________________________________
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