NAME DATE PER. GEOMETRY PRE-AP FALL FINAL EXAM …amchsgeometrypreap.weebly.com/uploads/1/1/0/1/... · Fall Final Exam Review Refer to the number line below to find the measures for

Fall Final Exam Review

NAME__________________________________DATE_______________PER._____

GEOMETRY PRE-AP FALL FINAL EXAM REVIEW

Part 1: Geometry Basics Match each of the following terms with its correct description.

________1. Point A. a point that divides a line segment exactly in half

________2. Line B. an exact location in space

________3. Plane C. has one endpoint and continues infinitely in one

direction

Coplanar ________4. Points

D. points that lie in the same line

Line ________5. Segment

E. a set of points in a row that continues infinitely in two directions

________6. Ray F. a set of points containing two endpoints and all of the

points between them

________7. Midpoint G. a flat surface that continues infinitely in all directions

________8. Coordinate H. points that lie on the same plane

________9. Collinear I. a number that identifies a point’s location

Using the figure below, name each of the following.

10. ____________ he intersection of M and L

11. ____________ A ray opposite DB

12. ____________ A plane containing CE

13. ____________ The intersection of L and CE


Refer to the number line below to find the measures for problems 14. – 16.

14. Find the distance between X and T.

15. Find the distance between Z and W.

16. What point(s) is/are two units from point U?

17. If A is between X and Y, and XA = 3x, AY = 2x + 5, and XY = 60, find the value of ‘x’.

18. Find the distance between the points E(-3, -4) and F(5, 4).

19. Find the distance between the points A(-3, 5) and B(0, 1).

Refer to the number line to find the coordinate of the midpoint of each segment.

20. 𝐴𝐶 21. 𝐵𝐷

Find the midpoint of the segment with the given endpoints.

22. (-7, 7) and (-9, 8) 23. (-3, 6) and (2, -8)

0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

A B C D E

0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

V W T S X Z U R Y


Find the indicated length.

24. F is the midpoint of 𝐸𝐺. If EF = 2x + 3 and EG = 6x – 3, find FG.

FG = ______________

25. F is the midpoint of 𝐸𝐺. If EF = x + 2 and FG = 2x – 6, find FG.

FG = ______________

PART 2: ANGLE BASICS Using the figure below, find the indicated measures.

26. mFEC = 32, find mCED.

mCED = __________

27. mCEA = (6x – 20), mAED = (3x + 18), and mCED = 151. Find the value of ‘x’.

x = __________

Use the figure below to answer the following questions.

28. Name a pair of adjacent, complementary angles.

29. Which angle is vertical to STR?

A

C

E

D

F

M

N P

Q

R S

T


30. The measure of PTR is twice the measure of

NTP. Find the measure of both angles.

31. Find ‘x’ if mMTN = (3x - 2) and

mNTP = (4x + 1).

32. Find ‘x’ if mNTP = (2x + 20) and

mSTR = (3x + 15).

In the figure below, 𝑩𝑨⃗⃗⃗⃗⃗⃗ and 𝑩𝑪⃗⃗⃗⃗⃗⃗ are opposite rays, and 𝑩𝑬⃗⃗⃗⃗⃗⃗ bisects ABD.

33. If mABE = (6x + 2) and mDBE = (8x – 14), then find

mABE.

mABE = __________

34. If mABD = (2y) and mDBC = (6y – 12), then find

mDBC.

mDBC = __________

35. If mABE = (12n – 8) and mABD = (22n – 11), then find

mEBD.

mEBD = __________

A

B

C

D E

M

N P

Q

R S

T


Match each description with its corresponding term. Write its corresponding letter in the blank provided.

______36. An angle with a measure between 0 and 90. A. angle

______37. Angles that have equal measures. B. right angle

______38. An angle with a measure of 90. C. vertex

______39. A ray that divides an angle into two congruent angles.

D. congruent angles

______40. An angle with a measure of 180 E. straight angle

______41. An angle with a measure between 90 and 180. F. angle bisector

______42. A figure formed by two rays that have the same endpoint.

G. adjacent angles

______43. Angles that have a common vertex and side, but share no interior points.

H. segment bisector

______44. A pair of angles with a sum of 180. I. acute angle

______45. Two non-adjacent angles formed by two intersecting lines.

J. midpoint

K. obtuse angle

L. complementary Angles

M. supplementary

angles

N. vertical angles

O. collinear

Answer the following.

_____________ 46.

Find the sum of the measures of the interior angles of an octagon.

_____________ 47.

Find the measure of each interior angle of a regular decagon.


_____________ 48.

Find the sum of the measures of the exterior angles of a 20-gon.

_____________ 49.

Find the measure of each exterior angle of a regular 15-gon.

PART 3: Conditional Statements & Proofs

50. Hypothesis:

If you complete your final exam reviews, then you will do well on your final.

51. Conclusion:

If you exempt your second period final, then you still need to show up for class.

52. Negation:

August is the hottest month.

53. Converse:

If you eat your ice cream too fast, then you’ll get a brain freeze.

54. Inverse: If you exempt your first period final, then you can leave school after lunch on Thursday.

55. Contrapositive: If you want to do well in geometry, then you will do your homework.


Tell which algebraic property is being displayed in each of the following.

56. ____________________ If n, then n = n.

57. ____________________ If x – 7 = 10, then x = 17.

58. ____________________ If a + 3 = 8, then a = 5.

59. ____________________ If a = 3 and b = 3, then a = b.

60. ____________________ If x + y = 7 and y = 3, then x + 3 = 7.

61. ____________________ If a = b, then 2a = 2b.

Fill in each statement with its corresponding reason in the two-column, algebraic proof. 62. Given: 𝑦(𝑥 − 7) = 42; 𝑦 = 3 Prove: 𝑥 = 21

STATEMENTS REASONS

PART 4: PARALLEL LINES

Use the figure below for problems 63. – 68. Identify each angle pair and tell whether they are congruent or supplementary.

63. TYPE:____________________

or supplements?

1 and 5

1 2

3 4

5 6

7 8


64. TYPE:____________________ ≅ or supplements?

4 and 5


2 and 8


6 and 7


3 and 5


6 and 8

Find the value of ‘x’ in each of the following.

69. x = ____________

70. x = ____________

(2x – 3)

135

(2x + 7)

103

1 2

3 4

5 6

7 8


Given 𝒍||𝒎, m1 = 98, and m2 = 40, find the measure of each angle.

71. _______________

m4 =?

72. _______________

m8 =?

73. _______________

m9 =?

Find the indicated value(s).

74. x = ___________

y = ____________

Find the values of ‘x’ and ‘y’.

75. x = ____________

Find the value of ‘x’.

76. x = ____________


77. x = ____________


l m a

b 1 2

3

4 5

6 7 8 9

(3y + 8) (4x + 9)

(19x + 10)

(3x – 50)

(2x – 5)

(6x –12)

2x

110

(4x – 10)


Use the pyramid below to answer questions 78 and 79.

78. _____________________ Name all pairs of parallel segments.

79. _____________________ Name a segment skew to

𝐴𝐸⃗⃗⃗⃗ ⃗.

PART 5: Triangle Basics Use the picture at the right to answer 80 – 83. 80. m = ____________

Classify:

Find the missing angle in

LMN and classify the triangle by angles.

81. m = ____________

Classify:

Find the missing angle in

TMO and classify the triangle by angles.

82. Sides:

Name the sides of LMN in order from smallest to largest.

83. Sides:

Name the sides in MOT from largest to smallest.

Determine whether it is possible to form a triangle with the given lengths of sides. If yes, classify the triangle by SIDES.

84. 5, 4, and 3 YES or NO Classify:




M

D

E A

R

L

M

N

O

T

67

80

75


Find the value of ‘x’ in each of the following.

88. _______________

89. _______________

90. ________________

91. _______________

𝐵𝐷 is an altitude in ABC, find the value of ‘x’ if mADB = (3x +15)°.

Part 6: Congruent Triangles Answer each of the following questions.

92. _______________

If BOY ≅ GAL, then 𝑌𝐵 ≅ __?__.

93. _______________

If QRS ≅ LMN, then Q ≅ __?__.

Determine whether the following pairs of triangles are congruent by SSS, SAS, ASA, AAS, HL or none.

94. __________

(x + 10) x

(x + 20)

(x – 42)

(x – 37)

x

82

x

A

B

D

C


95. __________

96. __________

Write a two-column proof for the problem below.

97. GIVEN: 𝑃𝑂 𝑄𝑅

𝑃𝑂 bisects QPR

PROVE: Q ≅ R

PART 7: Similarity Find each value as indicated.

98. ______________

Given that 𝐵𝐸 ║ 𝐶𝐷, AC = 8, AE = 6, ED = 3, find AB.

A

B E

C D

Q

P

R O


99. ______________


100. _____________

Use the figures below to answer questions 101 – 103.

101. ___________

What is the similarity ratio of ΔABC and ΔDEF?

102. ___________

What is the value of ‘x’?

103. ____________

What is the value of ‘y’?

PART 8: RIGHT TRIANGLES Find the value of ‘x’ in each of the following. All answers should be EXACT.

104. x = ________

105. x = ________

x

5

12

x

x

14

x + 2

3x – 4

2

3

2x + 3

2x + 5

A

B

C

2.5 in 3

4 in. D

E

F

x y

14 in.

~


Determine if the given lengths can form a triangle. If yes, classify it by ANGLES.

106. YES or NO Classify:

6, 7, and 8

Find the indicated value in each of the following.

107. Find the EXAXT value of AB. AB = __________

108. Find the EXACT value of AB. AB = __________

109. Find the EXACT value of BC. BC = __________

110. Find the value of BC. BC = __________

111. Find the value of BC. BC = __________

112. Find the EXACT value of the diagonal. Diagonal = ________

113. Find the EXACT values of BD and CD. BD = _________ CD = _________

A

8ξ𝟐

45 B

C

45

6

A C

B

30 14

B

A C

16 60

A

B

C

ξ𝟑

60

A C

B

10

12 12

12

B

A C D


Find the indicated values.

114. sinA = _________

cosA = _________ tanA = __________

Find the indicated trigonometric ratios for the triangle below.

115. x = __________


Convert to radians or degrees. Leave radian answers in terms of π.

116. 125o 117.

3𝜋

4

Determine the quadrant in which the terminal side of the given angle lies.

118. −2𝜋

3

119. 268o

Find two angles, one in the positive direction, and one in the negative direction, which are coterminal with the given angle.

120. 5𝜋

3 121. −

3𝜋

4

Find the indicated value.

121. A plane is flying at an altitude of 14,500 ft. The angle of depression from the plane to the control tower is 15°. What is the horizontal distance from the plane to the tower? Round to the nearest foot.

Answer: ___________

A

B C

8

6

10

42

x 9

Documents

NAME DATE PER. GEOMETRY PRE-AP FALL FINAL EXAM …amchsgeometrypreap.weebly.com/uploads/1/1/0/1/... · Fall Final Exam Review Refer to the number line below to find the measures for