Geometry Name: __________________________ Final Exam Review Packet Date: _____________ Period: ______

Multiple-Choice: Choose the best answer. 1. Two friends decide to go to the movies. Given the choice between a comedy, drama, action, or horror, they decide on a comedy. Which of the following events is the complement of this event?

A. Drama B. Action C. Horror D. All the above 2. The following balls are placed in an urn: 5 red, 6 yellow, 4 blue, and 3 green. One ball is randomly drawn from the urn. What is the probability that the ball is either red or blue?

A. 1/3 B. 2/3 C. ½ D. 3/4 Short-Answer: Write answers clearly and concisely. Show all work. Round all answers to the hundredths place. 3. Explain why there are 20 possible outcomes in the sample space for rolling a ten-sided die and flipping a coin? 4. The lattice diagram below represents the sample space for two dice thrown.

a) Using the lattice above, find the probability that the sum of two die rolled will be 10.

b) Using the lattice, determine the probability that the sum of the numbers rolled is either an odd number or the first die is a multiple of three.

Dice Lattice

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

5. A faculty advisor at Ridge High School surveyed 100 students about their preference for a social event. Fifty-five males were surveyed. Of those, 35 prefer bowling and a total of 38 prefer dance.

a) Complete the two-way frequency table below.

Bowling (B) Dance (D) Total

Males (M)

Females (F)

Total

b) Find ( )P D

c) Find ( )P F B

d) Find ( )P M D

6. You are choosing a one topping pizza with thin (T) or hand-tossed (H) crust and a choice of pepperoni (P), bacon (B), mushrooms (M), green peppers (G) or onions (O). NOTE: pepperoni and bacon are “meats”. Be sure to use set notation when needed.

a) List the sample space (all possible outcomes). Use set notation.

b) Create a Venn diagram with the sample space above using the outcomes of thin crust and meat.

c) Find ( ) 'Thin Meat

d) What does the set ( )Thin Meat represent?

e) What does the set Thin Meat represent?

Thin Meat

Multiple-Choice: Choose the best answer. 7. Which of the following events are independent, given 𝑃(𝐴), 𝑃(𝐵), and 𝑃(𝐴 𝑎𝑛𝑑 𝐵)?

A) 𝑃(𝐴) = 0.2; 𝑃(𝐵) = 0.25; 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0.5 B) 𝑃(𝐴) = 0.03; 𝑃(𝐵) = 0.9; 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0.12 C) 𝑃(𝐴) = 0.4; 𝑃(𝐵) = 0.09; 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0.036 D) 𝑃(𝐴) = 0.35; 𝑃(𝐵) = 0.35; 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0.7

8. A survey is given to upperclassman and asks if they have a driver’s license or not. The results are shown in the table below.

Has License Does Not Have License Junior 4 9 Senior 11 1

What is the probability that a randomly selected person has a license, given that the person selected is a junior?

A) 0.51 B) 0.27 C) 0.31 D) 0.73 9. Assume the following events are independent:

The probability that a high school senior will graduate with a scholarship is 0.84 The probability that a high school senior graduate with a scholarship and go to college is 0.35

What is the probability that a high school senior will go to college, given that he/she graduated with a scholarship?

A) 0.46 B) 0.49 C) 0.40 D) 0.42 10. Which of the following events would be considered dependent? A) Learning to ride a bicycle and learning to play the piano. B) How long it takes you to walk to school and how long each of your classes lasts. C) If you remove a king from the deck and then replace it and the probability of then drawing a two. D) How many minutes you spend practicing your homework and how well you do on that test. 11. There are 25 students in the room. There are 18 girls and 7 boys. What is the probability of choosing one girl and then one boy?

A) 21

100 B)

1

4 C)

9

50 D)

126

625

Short-Answer: Write answers clearly and concisely. Show all work. Round all answers to the hundredths place.

12. The following events are independent. Find the missing values. Show all work.

a) Given 𝑃(𝑆) = 0.52 and 𝑃(𝐵) = 0.3, find 𝑃(𝑆 ∩ 𝐵) = _____________________

b) Given 𝑃(𝑀) = 0.75 and 𝑃(𝑀 ∩ 𝐿) = 0.185, find 𝑃(𝐿) = _____________________

13. Use the data in the table below, which shows the employment status of individuals in a particular town by age group.

Age Group Full Time Part-Time Unemployed Total 0-17 86 58 110 254 18-25 23 33 98 154 26-34 47 45 4 96 35-49 28 78 11 117 50+ 29 11 2 42 Total 213 225 225 663

a) A person from the town is randomly selected, find the probability that the individual is 50+ years

of age.

b) What is the probability that the individual is between 26 and 34 years of age, given that he or she is employed part-time?

14. The table below shows the political party registration by gender of all 500 registered voters in Franklin Township.

Party W Party X Party Y Total Female 117 128 65 310 Male 67 103 20 190 Total 184 231 85 500

a) Given that a randomly selected person is registered for Party W, what is the probability that he is a

male?

b) Given that a randomly selected person is registered for party W, what is the probability that she is female?

c) Using parts (a) and (b), is a male or female more likely to be registered for Party W? Explain your reasoning.

d) Among the registered voters of Franklin Township, are the events “is a female” and “is registered for Party X” independent? Justify your answer based on probabilities calculated from the table above. Show all work.

Multiple Choice: Choose the best answer.

Use the diagram below to answer the questions 15-17.

15. Find the distance for segment BC.

A) 7 B) 7 2 C) 49 D) 98

16. Find the distance for segment DC.

A) 2 5 B) 5 C) 5 2 D) 50

17. Find the area of the rectangle DCBA.

A) units235 B) units250 C) units260 D) units270 18. Which expression represents the area of the triangle?

A) pr B) pr1

2 C) p r D) pr2

19. Look at the coordinates for triangle XYZ.

X(-3,-1) Y(2,3) Z(2,-1)

Using the distance formula, find the perimeter of triangle XYZ?

A) 9 units B) 10 units C) 9 41 units D) 50 units

Z B

AXY

Matching: Match the definition with the correct vocabulary word listed below.

A. Equilateral Polygon H. Regular Polygon

B. Equiangular Polygon I. Quadrilateral

C. Complementary Angles J. Angle Bisector

D. Supplementary Angles K. Segment Addition Postulate

E. Heptagon L. Angle Addition Postulate

F. Hexagon M. Acute Angle

G. Pentagon N. Obtuse Angle

20. An angle with measure less than 90 degrees is called ________________________. 21. A polygon with seven sides is a(n)_________________. 22. Two angles that measure to 180 degrees are ___________________. 23. A polygon with all congruent sides and angles is _________________.

24. Mark the figure with the given information.

X is the midpoint of AY , ,XZ XB XZB XBZ

25. Use the figure at the right to correctly name a pair of each.

a) Which angle is vertical to angle FDE ________________

b) Name a obtuse angle __________

c) What segment is congruent to segment AD? _________

26. If AB = 4 cm, what is the perimeter of regular octagon ABCDEFGH?_________ cm 27. Find the midpoint between the two points below __________________

(7x+55)°(5x+17)°A D

B

E

C

B

A

C

D

E

G

F

28. Find the value of x. Then find the measure of angle ACB.

x = _________

________m ACB

29. Let EF = 2x – 13, FG = 2x – 6, and EG = 13. Find the indicated variable. Then find the measure of EF.

x = ___________ EF = __________

30. If BC is the angle bisector of ABD , 3 8m ABC x , and 2 1m CBD x , solve for x. Then find the measure of ABD .

x = ______________

m ABD = _____________

31. Multiple Choice: Complete the proof below.

Given: 1 5 Prove: 1 7

Statements Reasons 1 5 Given 5 7 1 7 Transitive Property of Congruence

A. Linear Pair Postulate

B. Vertical Angle Congruence Theorem

C. Angle Addition Postulate D. Definition of Congruent Angles

B

A

C

D

Fill in the blank: Using the word bank below, complete the proof below.

Definition of Congruent Angles Definition of Congruent Segments Vertical Angles are Congruent Addition Property Definition of Supplementary Angles Subtraction Property

32. In this diagram, line m intersects line n.

Prove: Vertical angles 1 and 3 are congruent.

Statements Reasons

Line m intersects line n Given

1 and 2 form a linear pair 2 and 3 form a linear pair

Definition of linear pair

m m1 2 180

m m2 3 180

Angles that form a linear pair have measures that sum to 180°

m m m m1 2 2 3 Substitution Property

m m1 3

1 3

33. Complete the proof below.

Given: BC is the angle bisector of ABD , (10 4)m ABC x , and 26m CBD

Prove: x = 3

Statements Reasons

Given

Given

Given

Def of Angle Bisector

Definition of Congruence

10x – 4 = 26

Addition Property

21

E

G

F

34. Complete the proof below.

Given: 1 (5 17)m x and 2 (3 5)m x

Prove: 1 122m

Statements Reasons

Given

Given

1m and 2m are supplementary Definition of Linear Pair

1 2 180m m

5x + 17 + 3x – 5 = 180

Simplify

8x = 168

Division Property

Substitution Property

35. Complete the proof below.

Given: EF = x + 8, FG = 4, and EG = 4x + 3 Prove: x = 3

Statements Reasons

EF = x + 8 Given

FG = 4 Given

EG = 4x + 3 Given

Segment Addition Postulate

Substitution Property

x + 12 = 4x + 3

Subtraction Property

9 = 3x

Division Property

36. Given the following points and the slope of each set of points, determine which two lines are parallel to each other. Be sure to use mathematical notation.

_________ _________

Justify your answer mathematically or using key vocabulary terms. 37. Determine whether the following lines are parallel, perpendicular or neither.

27

5y x 5 2 14 x y

Explain why. Be sure to use mathematical language. 38. Write the equation of the line (in slope-intercept form) that is perpendicular to 4 3 y x and passes

through the point (8, -7). 39. Given a line passes through the points (7, 2) and (9, 3), write the equation of the line (in slope intercept form) parallel to the original and passes through the point (12, -6).

40. Multiple Choice: For what value of n are the lines 4 6 7y x and 1012

ny perpendicular?

A) -12 B) -8 C) 8 D) 12

A(-8, -1) and B(-3, -4)

Slope of 3

5AB

C(11, 3) and D(5, -12)

Slope of 5

2CD

E(-9, 1) and F(-7, 6)

Slope of 5

2EF

G(5, 0) and H(8, 5)

Slope of 5

3GH

41. Multiple Choice: The equation of line a (shown to the right) is 1

22

y x .

Which is an equation of the line that is perpendicular to line a and passes through the point (2, -3)?

A) 1

32

y x B) 1

72

y x

C) 2 7y x D) 2 3y x

42. Use the diagram to the right to answer a and b below. Assume ||l m .

a) If m2 = 5x+15 and m5 = 75⁰,

Angle relationship: _________________________________ x ________ m2 = ________

b) If m1 = 120⁰ and m6 =16x+8,

Angle relationship: _________________________________

x ________ m6 = ________ 43. Multiple Choice: Which pair of triangles is congruent by ASA?

44. Multiple Choice: In the diagram below, four pairs of triangles are shown. Congruent corresponding parts are labeled in each pair. Using only the information given in the diagrams, which pair of triangles cannot be proven congruent?

A) B) C) D)

45. Multiple Choice: In this diagram, PX TY and .P T Which additional information is sufficient to prove that QYP is congruent to ?SXT

A) XR YR

B) QR SR

C) RYX RXY D) RXP RYT 46. Determine which answer below is depicted in the triangles to the right. A) BAC and SRQ are not congruent

B) ;BAC SRQ because of SSA

C) ;BAC SRQ because of SAS

D) ;BAC SRQ because of ASA

47. Given QRS HIJ , then QSR is congruent to ____________.

A) HIJ B) HJI C) JHI D) JIH 48. Given PQR TUV , PQ = 3x + 4, and TU = x + 12. What is the measure of segment TU?

A) TU = 2 B) TU = 4 C) TU = 14 D) TU = 16

(2x - 6)°

86°

A

C B

p

q

e

c

fa

gb

hd64

(x+77)°(47+x)°

70°

C

B

A

K N

L

M

(6x - 9)º

(4x + 7)º

118º

(

49. Use the diagram below to solve for each missing angle. Assume ||p q .

a _________ b _________ c _________ d _________

e _________ f ________ g _________ h _________

50. Multiple Choice: Given the figure below with measurements of ∡𝐷𝐴𝐵 = 60°, ∡𝐴𝐵𝐷 = 75°, and ∡𝐵𝐷𝐶 = 25°. Name ∆𝐷𝐵𝐶. A) Obtuse isosceles triangle B) Acute scalene triangle C) Obtuse scalene triangle D) Right scalene triangle 51. In each figure below, solve for the missing variable and angle. a) b) x = ____________ mA= ___________ x = ____________ mABC= _____________ c) x =__________ m L = _____________

A B C

D

60º 75º

25º

52. Multiple Choice: In diagram, STU is an isosceles triangle where ST is congruent to UT . The paragraph proof shows that S is congruent to U .

What is missing in the proof? A) CPCTC B) Definition of right angles C) Reflexive Property D) Symmetric Property 53. Complete this proof of the converse of the isosceles triangle theorem. Choose from the Reasons listed below to complete the proof.

Given: ,CAB BCA BD AC

Prove: ∆𝐴𝐵𝐶 is isosceles

Statement Reason

CAB BCA Given

𝐵𝐷̅̅ ̅̅ ⊥ 𝐴𝐶̅̅ ̅̅ Given

BDA and BDC are right angles

Definition of Perpendicular lines

BDA BDC

𝐵𝐷̅̅ ̅̅ ≅ 𝐵𝐷̅̅ ̅̅

∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷

𝐴𝐵̅̅ ̅̅ ≅ 𝐵𝐶̅̅ ̅̅

∆𝐴𝐵𝐶 is isosceles Definition of isosceles triangle

54. Molly drew the following pictures. According to the Angle-Side-Angle (ASA) theorem, where should Maria draw tick marks to show that ∆𝐴𝐵𝐶 ≅ ∆𝑀𝑇𝑅? Mark or name where the marks should go.

A. SSS Congruence B. SAS Congruence C. AAS Congruence D. SSA Congruence E. Definition of an isosceles triangle F. Right Angles are Congruent G. Vertical Angles are Congruent H. Reflexive Property I. CPCTC J. Definiton of Angle Bisector

It is given that ST is congruent to .UT Draw TV such that V is on SU and TV bisects .T By definition

of an angle bisector, STV is congruent to .UTV By the _________________, TV is congruent to .TV Triangle STV is congruent to triangle UTV by SAS. S is congruent to U by CPCTC.

55. According to the Angle-Angle-Side (AAS) theorem, where should Molly draw tick marks to show that ∆𝐺𝐸𝐹 ≅ ∆𝑃𝑅𝑄? Mark or name where the marks should go. 56. Given the following information, determine if the two triangles are congruent. If so, complete the congruence statement. a) b) QRS ______________ by ________ SRT ______________ by ________

57. Given the following, mark the figure below. Then determine if the triangles are congruent. If so, state the congruence statement.

a) Given: AB CD , AB CD , b) Given: CD bisects C

EC CD , A D AC BC ABC ____________ by ________ ACD _______________ by ________

CA

B

D

E

58. ABC is congruent to MNP . Name the appropriate corresponding sides and angles that show the triangles are congruent by SAS. M ( -8,-4) A (8, -4) P (-2,-4) C (2, -4) N (-2, 5) B (2, 5) _____________ ≅ ______________ _____________ ≅ ______________ _____________ ≅ ______________ 59. Complete the proof below.

Given: AD BC and CD AB .

Prove: ABD CDB

Statement Reason

1. AD BC 1.

2. 2.

3. 3. Reflexive Property

4. ABD CDB 4.

60. Complete the following proof below.

Given: ||AB DE and AB DE

Prove: BC DC

Statement Reason

1. ||AB DE 1.

2. 2.

3. 3.

4. 4. Vertical Angles are Congruent

5. ABC EDC 5.

6. BC DC 6.

61. Determine if the two triangles are similar. If so, state the similarity statement and state how you know they are similar (SSS~, SAS~, AA~). Justify your conclusions. (a) (b) i. Show work: i. Show work:

ii. Are the triangles similar? _______ ii. Are the triangles similar? _______ iii. If yes, then how? _____________ iii. If yes, then how? _____________

iv. If yes, then complete the similarity iv. If yes, then complete the similarity statement: _______STU statement: _______ABC

(c)

i. Show work: ii. Are the triangles similar? _______ iii. If yes, then how? _____________

iv. If yes, then complete the similarity statement: _______JKL

55

15x + 5

30

33

R

P Q

L

J K

149

18

x + 5

117

K

M L

F E

62. The triangles below are similar, solve for x.

(a) JKL RQP (b) KFE KML

x = __________ x = _____________

(c) RST RGH

x = __________

63. Given: ST PQ , RS= 8, SP= 12, and RT= 4. What is the measure of segment TQ?

Show your work to defend your answer:

TQ = _____________

8x + 7

42

98

91

R

T

S

G

H

64. Given QRS QTU . If k = 4.8 cm, j = 4 cm, m = 3.6 cm, and f = 6 cm,

what is the measure of h? Show all work. (3 points) h = __________ 65. Complete the two-column proof below.

Given: A C Prove: ∆𝐴𝐵𝐸~∆𝐶𝐷𝐸.

Statements Reasons

1. 1. Given

2. 2.

3. ∆𝐴𝐵𝐶~∆𝐶𝐷𝐸 3.

66. Multiple Choice: Use this triangle to answer the question.

This is a proof of the statement “Is a line is parallel to one side of a triangle and intersects the other two sides at distinct points, then it separates these sides into segments of proportional lengths.”

Which reason justifies Step 2?

A. Alternate interior angles are congruent. B. Alternate exterior angles are congruent. C. Corresponding angles are congruent D. Vertical angles are congruent.