E GF

S UT

5x 2x + 15

Semester 1 Final Exam Review

Use the figure at the right to answer questions #1-7.

1. Name the plane represented by the front of the prism.

2. What is the intersection of planes ACDB and DHFB?

3. What is the intersection of and

4. List all lines parallel to

5. List 4 lines skew to

6. Name a fourth point in plane ACF.

7. Name a fourth point in plane DHB.

In #8-11, use the diagram shown at the right.

8. Name the line segments skew to

9. What is the intersection of plane HGCD and ABDC?

10. List all segments parallel to

11. What plane is parallel to plane HGDC?

12. If EF = 3x – 16, FG = 2x – 6 and EG = 18, find x, EF, and FG.

13. If T is the midpoint of , find the values of x and ST.

14. Use the figure to find each of the following.

a. x

b. MR

c. RP

E

F

G

H

15. Are the points G, F, and E collinear? If so, name the line on which

they lie.

16. If T is the midpoint of find the values of x and ST. The diagram is not to scale.

17. If and , then what is the measure

of The diagram is not to scale.

Find the distance between each set of points to the nearest tenth.

18. M(3, 2), N(7, 9) 19. , D(5, 5)

Find the midpoint of the line segment with the given endpoints.

20. (-4, 8) (12, 0) 21. (10, -5) (-3, -7)

Identify the hypothesis and conclusion of the following conditionals.

22. If 3x + 7 = 19, then x = 4.

23. We will not go outside today if it is raining.

Show the conditional is false by finding a counterexample. 24. All fruit are red.

25. If it is not a weekday, then it is Sunday.

26. A number divisible by 4 is also divisible by 6.

S UT

4x 3x + 21

Use the Law of Detachment to find a conclusion. If it is not possible, then write not possible.

27. If we have a snow day, then I am staying in my pajamas all day. We have a snow day.

28. If a student wants to go to the University of Michigan, then the student must study hard.

Neil wants to go to the University of Michigan. Use the Law of Syllogism to draw a conclusion.

29. If it is hot outside, then we will go to the beach. If we go to the beach, then we will go swimming.

30. If you live in Grand Rapids, then you live in Michigan. If you live in Michigan, then you live in the United States. Write the converse of the conditional.

31. If it is a rose, then it is a flower.

32. If x + 1 = 8, then x = 7.

Find the value of the variable.

33. 34.

35.

This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways.

36. How are related?

37. How are related?

Use the picture shown at the right to answer the questions if the lines are parallel.

38. In the picture shown, if , then what is the

39. In the picture shown, if , then what is the

40. In the picture shown, if , then what is the

41. How are 6 and related?

42. How are and related?

43. Find the value of the variable. 44. Find the missing angle measure in the triangle.

45. Find the values of variables.

5

3 4

1 2

6

7 8

46. Find the value of x if and .

47. Find the value of the variable.

48. Find the What theorem or postulate did you use?

In #49-52, ABCD .

50. 51. 52.

In the problems below, tell which theorem or postulate you could use to prove the triangles

are congruent. Then, write a congruency statement.

53. 54.

55. 56.

1 2

3 4

5 6

7 8

l

m

57. Find the value of all of the variables.

58.. If , RS = 5x + 6, and LM = 7x – 2, find the value of x and RS. HINT: DRAW AND LABEL

A PICTURE.

59. Find the value of the variables.

60. What is the measure of the base angles 61. Find the value of the variables.

of the triangle shown?

62. Find the value of the variable.

d°

e°f°

b

c

g

5

12

13

34°

56°

63. Given: , 64. Given:

Prove: Prove:

65. Name a median for

66. B is the midpoint of D is the midpoint of and AE = 29. Find BD. The diagram is not to scale.

E D

C

H

F G

|

|

))

A E

C

B D

67. B is the midpoint of and D is the midpoint of Given and solve for x.

68. Find the value of x.

69. Q is equidistant from the sides of Find the value of x. The diagram is not to scale.

70. In ABC, G is the centroid and BE = 21. Find BG and GE.

A

C

E

B D

18

3x – 6

S

Q

T

R

|

|

|

|

29°

(5x

–11)

°

C

FA

D

E

BG

71. In G is the centroid and AG=22, find GD and AD.

72. bisects Find FG. The diagram is not to scale.

73. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.

74. Find the length of , given that is a median of the triangle and AC = 26.

C

FA

D

E

BG

D

F

E

G

))

n + 6

3n – 4

180 ft

A C

D

B

75. Find the value of x. The diagram is not to scale.

76. Points B, D, and F are midpoints of the sides of EC = 43 and DF = 18. Find AC. The diagram is not

to scale. (HINT: label the picture!)

Find the values of the variables. Then find the lengths of the sides of quadrilateral.

77. rhombus ABDC

Find the values of x and y for which the figure must be a parallelogram.

78. 79.

39

39

27 27

32

x

E

C

A

D

FB

||

| | ||

y – 5 x + 4

2x + 3 x + 6

3 4

2 1

Decide whether the quadrilateral is a parallelogram. Explain your answer.

80. 81. 82.

83. Isosceles trapezoid ABCD has legs and and base AB = 3y – 2, BC = 3y – 5 , and CD = 4y

– 17. Find the value of the variable. (HINT: DRAW IT OUT.)

84. Find the values of the variables AND the lengths of the sides of the kite.

85. Find all of the missing angles.

86. For the parallelogram shown at the right, if and

solve for x and find the measures of the missing angles.

87. JKLM is a rectangle. JL = 5x + 2 and KM = 7x – 14. Find the value of x and the length of each

diagonal.

88. In the trapezoid below, find the values of a and b.

89. Find the missing angle measures in the kite shown.

90. Find the values of the variables in the parallelogram.

91. In the figure, the horizontal lines are parallel and AB = BC = CD. Find MJ.

41° b°

111°a°

x°y°

z°

11537

6

M A

L B

K C

J D

92. Find the value of the variables.

93. Find the missing angle measures in the kite below.