Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Geometry First Semester Final Exam Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1. Find m∠1 in the figure below. PQ→←

and RS→←

are parallel.

a. 121° c. 59°b. 31° d. 131°

2. Which is the appropriate symbol to place in the blank? (not drawn to scale) AB __ AO

a. < c. =b. > d. not enough information

3. Find the value of x:

a. 88° b. 145° c. 35° d. 127°

2

4. If m∠AOC = 48° and m∠BOC = 21°, then what is the measure of ∠AOB?

a. 24° b. 32° c. 27° d. 29°

5. ΔABD ≅ ΔCBD. Name the theorem or postulate that justifies the congruence.

a. HL b. SAS c. AAS d. ASA

6. Find the value of y that will allow you to prove that CD→←

below is parallel to EF→←

if the measure of ∠1 is 4y − 12ÊËÁÁ

ˆ¯̃̃° and the measure of ∠2 is 48°. (The figure may not be drawn to scale.)

a. 22 c. 23b. 69 d. 36

3

7. ΔABD ≅ ΔCBD. Name the theorem or postulate that justifies the congruence.

a. AAS b. SAS c. HL d. ASA

8. In the diagram below, KF→←

is the perpendicular bisector of GH. Then ∠KGF ≅ .

a. ∠FKG b. ∠KF c. ∠KHF d. ∠KFH

9. The distance between points A and B is _______.

a. 13 b. 11 c. 85 d. 85

4

10. Which postulate or theorem can be used to determine the length of RT?

a. ASA Congruence Postulate c. SSS Congruence Postulateb. AAS Congruence Theorem d. SAS Congruence Postulate

11. For the trapezoid shown below, the measure of the median is _______.

a. 29b. 58c. 25d. 30

12. Find the value of x:

a. 92° b. 144° c. 128° d. 36°

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13. Find the values of x and y.

a. x = 16°, y = 98° c. x = 82°, y = 98°b. x = 16°, y = 82° d. x = 82°, y = 62°

14. What is the measure of each base angle of an isosceles triangle if its vertex angle measures 44 degrees and its 2 congruent sides measure 18 units?

a. 68° b. 46° c. 136° d. 44°

15. If KF→←

is the altitude of GKH and GK ≅ HK, then ∠GKF ≅ ______.

a. ∠KHF b. ∠FGK c. KF d. ∠HKF

6

16. Name an angle complentary to ∠COD.

a. ∠COB c. ∠DOE or∠AOCb. ∠DOB d. ∠DOC or∠AOE

Refer to the figure below for questions 13 and 14.

Given: AF ≅ FC, ∠ABE ≅ ∠EBC

17. An altitude of ΔGCF is ____.a. CF

→←

b. FG c. CD d. GF→←

18. A perpendicular bisector of ΔABC is ____.a. BE

→←

b. BF c. BD d. GF→←

19. In the figure, ∠6 and∠2 are _____________.

a. alternate interior angles c. alternate exterior anglesb. consecutive interior angles d. corresponding angles

7

20. Two sides of a triangle have sides 4 and 13. The length of the third side must be greater than _____ and less than ____.a. 4, 13 b. 9, 17 c. 8, 18 d. 3, 14

21. If AB = 14 and AC = 27, find the length of BC.

a. 14 b. 41 c. 13 d. 3

22. Which best describes the relationship between Line 1 and Line 2? Line 1 passes through 2, −7Ê

ËÁÁˆ¯̃̃ and 4,−3Ê

ËÁÁˆ¯̃̃

Line 2 passes through −4,9ÊËÁÁ

ˆ¯̃̃ and −2,13Ê

ËÁÁˆ¯̃̃

a. perpendicularb. They are the same line.c. paralleld. neither perpendicular nor parallel

23. Which step in an indirect proof (proof by contradiction) is, “point out the assumption must be false and therefore the conclusion must be true”?a. first c. thirdb. second d. none of the above

24. If m∠GOH = 24° and m∠FOH = 50°, then what is the measure of ∠FOG?

a. 31° b. 28° c. 23° d. 26°

8

25. Refer to the figure.

The longest segment is ______.

a. MP b. NM c. ML d. LN

26. For parallelogram PQLM below, if m∠PML = 83°, then m∠PQL =______ .

a. m∠PQMb. 83°c. 97°d. m∠QLM

27. ∠1 and∠2 are supplementary angles. ∠1 and∠3 are vertical angles. If m∠2 = 72°, what is m∠3 ?

a. 18° c. 108°b. 72° d. 28°

28. Let B be between C and D. Use the Segment Addition Postulate to solve for w.CB = 4w− 4BD = 2w− 8CD = 24

a. w = 6 b. w = 10 c. w = –2 d. w = 4

9

29. In the figure, ∠8 and∠2 are __________.

a. alternate exterior angles c. corresponding anglesb. consecutive interior angles d. alternate interior angles

30. What is the measure of each base angle of an isosceles triangle if its vertex angle measures 42 degrees and its 2 congruent sides measure 17 units?

a. 138° b. 69° c. 42° d. 48°

31. In the figure shown, m∠CED = 63°. Which of the following statements is false?

a. ∠AED and∠BEC are vertical angles.b. m∠BEC = 107°c. ∠BEC and∠AEB are adjacent angles.d. m∠AEB = 63°

10

32. If RS = 51 and QS = 87.3, find QR.

a. 36.3 b. 26.3 c. 51 d. 138.3

33. If ON =6x − 2, LM =7x + 5, NM =x + 4, and OL =7y + 4, find the values of x and y given that LMNO is a parallelogram.

a. x = 17

; y = 1

b. x = -7; y = −1

c. x = -3; y = − 37

d. x = 13

; y = 73

34. Find the value of the variables in the parallelogram.

a. x = 65°, y = 21°, z = 138°b. x = 21°, y = 65°, z = 138°c. x = 42°, y = 8°, z = 130°d. x = 8°, y = 42°, z = 130°

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35. Solve for x.

a. 3 c. 1b. 6 d. 2

36. Use the figure below to solve for x.∠G = x°∠O = (2x + 21)°

a. 23 b. 33.5 c. 53 d. 67

37. A line L1 has slope 49

. The line that passes through which of the following pairs of points is parallel to

L1 ?a. (6, –3) and (2, 6) c. (–5, 2) and (6, 6)b. (12, –1) and (2, 8) d. (–3, 2) and (6, 6)

38. Given: AE→

bisects ∠DAB . Find ED if CB = 12 and CE = 16. (not drawn to scale)

a. 28 b. 192 c. 20 d. 4

12

39. Let E be between F and G. Use the Segment Addition Postulate to solve for u.FE = 7u− 6EG = 2u− 21FG = 36

a. u = 4 b. u = 7 c. u = 11 d. u = –3

40. Which best describes the relationship between the line that passes through (4, 4) and (7, 6) and the line that passes through (–3, –6) and (0, –4)?a. parallelb. neither perpendicular nor parallelc. same lined. perpendicular

41. In the figure, l Ä n and r is a transversal. Which of the following is not necessarily true?

a. ∠8 ≅ ∠2 c. ∠5 ≅ ∠3b. ∠2 ≅ ∠6 d. ∠7 ≅ ∠4

Short Answer

42. Find the slope of a line perpendicular to the line containing the points (12, -8) and (5, –4).

43. ∠1 and∠2 form a linear pair. m∠1=36°. Find m∠2.

44. Find the coordinates of the midpoint of the segment with the given pair of endpoints.J(6, 6); K(2, –4)

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45. Write the contrapositive of the following statement. If a number is not divisible by two, then it is not even.

46. m∠RPQ = (2x + 7)° and m∠OPQ = (7x − 3)° and m∠RPO = 67°. Find m∠RPQ and m∠OPQ.

47. Use the Distance Formula to determine whether ABCD below is a parallelogram.

14

48. Line l is the perpendicular bisector of MN.Find m∠M.

49. Two sides of a triangle have lengths 14 and 10. What are the possible lengths of the third side x?

50. Two sides of a triangle have lengths 28 and 67. Between what two numbers must the measure of the third side fall?

51. If m∠AOB = 27° and m∠AOC = 49°, then what is the measure of ∠BOC?

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52. Find the value of x.

53. ∠1 and∠2 are supplementary angles. ∠1 and∠3 are vertical angles. m∠2=67°. Find m∠3.

54. Decide if the argument is valid or invalid. If the argument is valid, tell which rule of logic is used. If the argument is invalid, tell why.

1) If a figure is a quadrilateral, then it is a polygon.2) I have drawn a figure that is a polygon. 3) Therefore, the figure I drew is a quadrilateral.

55. From the given true statements, make a valid conclusion using either the Law of Detachment or the Law of Syllogism:

1) If Ahmed can get time off work, he will go to Belize.2) If Ahmed goes to Belize, Jake will go with him. Ahmed will get time off work.

56. Decide if the argument is valid or invalid. If the argument is valid, tell which rule of logic is used. If the argument is invalid, tell why.

1) If today is a holiday, then we do not have school.2) Today is not a holiday.3) Therefore, we do have school.

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57. Given: Trapezoid ABCD with median EF. If AB = 19 and DC = 27, find the length of EF.

58. Write the inverse of the following statement. If a number is not even, then it is not divisible by two.

59. Decide whether Line 1 and Line 2 are parallel, perpendicular, or neither.Line 1 passes through (1, 2) and (–3, 4)Line 2 passes through (–3, 7) and (–1, 3)

60. m∠QOP = (2x + 6)° and m∠NOP = (9x − 1)° and m∠QON = 60°. Find m∠QOP and m∠NOP.

17

61. Identify the hypothesis and conclusion of the statement.If tomorrow is Friday, then today is Thursday.

62. Use the Law of Detachment to write the conclusion to be drawn from the two pieces of given information:

1) If you drive safely, then the life you save may be your own.2) Shani drives safely.

63. Solve for x:

64. ∠1 and ∠2 are complementary, and ∠2 and ∠3 form a linear pair. If m∠3 = 140°, what is m∠1? Explain your reasoning.

65. Tell whether the converse of the following statement is True or False. If it is false, give a counterexample. "A number is divisible by 2 if the number is divisible by 4."

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66. Find the measures of all three angles of the triangle.

67. Solve for x.

68. If QR is an altitude of ΔPQR, what type of triangle is ΔPQR?

69. Line l is the perpendicular bisector of MN.Find the value of x.

19

70. Find AB and BC in the situation shown below.

AB = x + 16, BC = 5x + 10, AC = 56

71. Use the distance formula to determine whether ABCD below is a parallelogram.

72. Find the midpoint of the segment with endpoints (1, 1) and (–15, 17).

20

73. ΔABC ≅ ΔCDA. What special type of quadrilateral is ABCD? Write a paragraph proof to support your conclusion.

74. Complete the statement for parallelogram ABCD. Then state a definition or theorem as the reason.AB ≅ _____

75. Given the following statements, can you conclude that Marvin listens to the radio on Monday night? If so, state which law justifies the conclusion. If not, write no conclusion.

(1) If it is Monday night, Marvin stays at home.(2) If Marvin stays at home, he listens to the radio.

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76. Identify the hypothesis and conclusion of the statement.If today is Tuesday, then yesterday was Monday.

77. Find the length of AB.

78. Using the diagram, give the coordinates of M if it is a midpoint.

79. The measure of an angle is 32° less than the measure of its supplement. Find the measure of the angle and the measure of its supplement.

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80. Identify the longest side of ΔABC.

81. QS→

bisects ∠RQTm∠RQS = (4x − 2)° and m∠SQT = (x + 13)°.

a. Write an equation that shows the relationship between m∠RQS and m∠SQT.b. Solve the equation and write a reason for each step.c. Find m∠RQT. Explain how you got your answer.

82. Given the following statements, can you conclude that Becky plays basketball on Wednesday night? If so, state which law justifies the conclusion. If not, write no conclusion. (1) If it is Wednesday night, Becky goes to the gym.(2) If Becky goes to the gym, she plays basketball.

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83. In the figure shown, m∠AED = 115°. True or False: ∠AEB and ∠AED are vertical angles and m∠AEB = 65°.

84. Name an angle supplementary to ∠2 in the figure below.

85. Tell whether the converse of the following statement is True or False. If it is false, give a counterexample. "If a number is even, then it is a multiple of 4."

86. Use the given angle measures to decide whether lines a and b are parallel. Write Yes or No.m∠3 = 95°, m∠6 = 95°

87. The midpoint of QR is M −1, 7ÊËÁÁ

ˆ¯̃̃. One endpoint is Q 7,9Ê

ËÁÁˆ¯̃̃. Find the coordinates of the other endpoint.

24

88. The measure of an angle is 22° less than the measure of its supplement. Find the measure of the angle and the measure of its supplement.

89. Given: Trapezoid ABCD with median EF. If AB = 21 and EF = 24, find the length of DC.

90. Given: SQ→

bisects ∠RST . Find QR if UT = 16 and UQ = 30. (not drawn to scale)

91. Given: SQ→

bisects ∠RST . Find QR if UT = 35 and UQ = 120. (not drawn to scale)

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92. Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent?

93. In the diagram, m∠BAC = 35°, m∠DCA = 105°, ∠CBD ≅ ∠BDA, and BA ≅ CD. Is enough information given to show that quadrilateral ABCD is an isosceles trapezoid? Explain.

94. Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent?

95. ΔTRI ≅ ΔANG. Also ∠T ≅ ∠G. What type of triangle is ΔTRI? Explain.

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96. HK and JL are angle bisectors. Which triangle congruence theorem or postulate could you use to prove that ΔHLJ≅ ΔKLJ? Explain your answer.

97. Which pair of lines is parallel if ∠1 is congruent to ∠7? Justify your answer.

98. Which pair of lines is parallel if ∠4 is congruent to ∠2? Justify your answer.

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99. a. Plot the following points in a coordinate plane: W (-3, -3), X (1, -6), Y (5, -3), Z (1, 0),b. Is WX congruent to YZ? Explain.c. Is there another pair of congruent segments? If so, name the segments and explain why they are congruent.

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Proofs

100. Given: ABCD is a rhombus.Prove: ΔACB ≅ ΔCAD

Statements Reasons

______________________________ ______________________________

______________________________ ______________________________

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______________________________ ______________________________

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101. Given: ED⊥EC; BD⊥BC; ED ≅BCProve: ΔCED ≅ ΔDBC

Statements Reasons

______________________________ ______________________________

______________________________ ______________________________

______________________________ ______________________________

______________________________ ______________________________

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______________________________ ______________________________

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102. Given: ΔABF ≅ ΔDEC and FB Ä ECProve: BCEF is a parallelogram.

Statements Reasons

______________________________ ______________________________

______________________________ ______________________________

______________________________ ______________________________

______________________________ ______________________________

______________________________ ______________________________

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103. Writing: Write a paragraph proof to show that ∠4 and ∠5 are supplementary if ∠3 ≅ ∠2.

Statements Reasons

______________________________ ______________________________

______________________________ ______________________________

______________________________ ______________________________

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______________________________

104. Complete the reasons of this proof.Given: AE || DC; AB ≅ DBProve: ΔABE ≅ ΔDBC

Statements Reasons

1. AE Ä DC; AB ≅ DB 1.

2. ∠A ≅ ∠D 2.

3. ∠ABE ≅ ∠DBC 3.

4. ΔABE ≅ ΔDBC 4.

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105. Given: VU ≅ ST and SV ≅ TUProve: VX = XT

Statements Reasons

______________________________ ______________________________

______________________________ ______________________________

______________________________ ______________________________

______________________________ ______________________________

______________________________ ______________________________

106. Provide the reasons for each statement in the proof.Given: m∠1 = m∠3Prove: m∠AFC = m∠DFB

Statement Reason

m∠1 = m∠3 ?

m∠1 +m∠2 = m∠3 +m∠2 ?

m∠1 +m∠2 = m∠AFC, m∠3 +m∠2 = m∠DFB ?

m∠AFC = m∠DFB ?

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107. Given: BD is the median to AC, AB ≅ BCProve: ∠CBD ≅ ∠ABD

Statements Reasons

______________________________ ______________________________

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108. Given: ΔABC is an equilateral triangle; D is the midpoint of ACProve: ΔABD ≅ ΔCBD

Statements Reasons

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109. Given: PR = 12

PT

Prove: R is the midpoint of PT

Statements Reasons

______________________________ ______________________________

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ID: A

1

Geometry First Semester Final Exam ReviewAnswer Section

MULTIPLE CHOICE

1. ANS: A STA: MI 9-12.G1.1.2 2. ANS: B STA: MI 9-12.L1.2.1 3. ANS: B STA: MI 9-12.G1.1.1 | MI 9-12.G1.2.1 | MI 9-12.G1.2.2 4. ANS: C 5. ANS: D STA: MI 9-12.G2.3.1 | MI 9-12.G2.3.2 6. ANS: D STA: MI 9-12.A1.2.1 | MI 9-12.A1.2.3 7. ANS: A STA: MI 9-12.G2.3.1 | MI 9-12.G2.3.2 8. ANS: C STA: MI 9-12.G1.2.5 9. ANS: C STA: MI 9-12.A1.2.9 | MI 9-12.G1.1.5 10. ANS: B STA: MI 9-12.G2.3.1 | MI 9-12.G2.3.2 11. ANS: A STA: MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3 12. ANS: D STA: MI 9-12.G1.1.1 | MI 9-12.G1.2.1 | MI 9-12.G1.2.2 13. ANS: B STA: MI 9-12.G1.2.1 | MI 9-12.G1.2.2 | MI 9-12.G1.3.1 14. ANS: A STA: MI 9-12.G1.3.1 15. ANS: D STA: MI 9-12.G1.2.5 16. ANS: A STA: MI 9-12.G1.1.1 17. ANS: B STA: MI 9-12.G1.2.5 18. ANS: D STA: MI 9-12.G1.2.5 19. ANS: D STA: MI 9-12.G1.1.2 20. ANS: B 21. ANS: C 22. ANS: C STA: MI 9-12.A1.2.9 | MI 9-12.A2.4.4 23. ANS: C STA: L4.3.2 24. ANS: D 25. ANS: C 26. ANS: B STA: MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3 27. ANS: C STA: MI 9-12.G1.1.1 28. ANS: A 29. ANS: A STA: MI 9-12.G1.1.2 30. ANS: B STA: MI 9-12.G1.3.1 31. ANS: B STA: MI 9-12.L4.3.3 32. ANS: A 33. ANS: B STA: MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3 | MI 9-12.G1.5.2 34. ANS: C

STA: MI 9-12.G1.1.2 | MI 9-12.G1.2.1 | MI 9-12.G1.2.2 | MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3

35. ANS: A STA: MI 9-12.A1.2.1 | MI 9-12.A1.2.3 | MI 9-12.G1.1.1 36. ANS: A STA: MI 9-12.G1.2.1 | MI 9-12.G1.2.2 37. ANS: D STA: MI 9-12.A1.2.9 | MI 9-12.A2.4.4 38. ANS: C STA: MI 9-12.L1.1.6 | MI 9-12.G1.2.3 | MI 9-12.G1.2.5 | MI 9-12.G1.3.1

ID: A

2

39. ANS: B 40. ANS: A STA: MI 9-12.A2.4.4 41. ANS: D STA: MI 9-12.G1.1.2

SHORT ANSWER

42. ANS: 74

STA: MI 9-12.A1.2.9 | MI 9-12.A2.4.4 43. ANS:

144°

STA: MI 9-12.G1.1.1 44. ANS:

(4, 1)

STA: MI 9-12.A1.2.9 | MI 9-12.G1.1.5 | MI 9-12.G1.4.2 45. ANS:

If a number is even, then it is divisible by two.

STA: MI 9-12.L4.2.4 46. ANS:

m∠RPQ = 21° and m∠OPQ = 46°

STA: MI 9-12.A1.2.1 47. ANS:

If ABCD is a parallelogram, then AB = DC. Since AB = 37 and DC = 40 , ABCD is not a parallelogram.

STA: MI 9-12.A1.2.9 | MI 9-12.G1.1.5 | MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3 | MI 9-12.G2.3.4

48. ANS: 68°

STA: MI 9-12.G1.2.1 | MI 9-12.G1.2.2 | MI 9-12.G1.3.1 | MI 9-12.G2.3.1 | MI 9-12.G2.3.2 49. ANS:

4 < x < 24 50. ANS:

39 < x < 95 51. ANS:

22° 52. ANS:

32°

STA: MI 9-12.G1.2.1 | MI 9-12.G1.2.2

ID: A

3

53. ANS: 113°

STA: MI 9-12.G1.1.1 54. ANS:

invalid; converse error (The figure could have been a triangle.)

STA: MI 9-12.L4.1.2 | MI 9-12.L4.2.1 | MI 9-12.L4.2.3 | MI 9-12.L4.2.4 | MI 9-12.L4.3.1 | MI 9-12.L4.3.3

55. ANS: Ahmed will go to Belize, and Jake will go with him.

STA: MI 9-12.L4.1.1 | MI 9-12.L4.1.3 | MI 9-12.L4.3.3 56. ANS:

invalid; inverse error

STA: MI 9-12.L4.1.2 | MI 9-12.L4.2.3 | MI 9-12.L4.2.4 | MI 9-12.L4.3.1 | MI 9-12.L4.3.3 57. ANS:

23

STA: MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3 58. ANS:

If a number is even, then it is divisible by two.

STA: MI 9-12.L4.2.4 59. ANS:

neither

STA: MI 9-12.A1.2.9 | MI 9-12.A2.4.4 60. ANS:

m∠QOP = 16° and m∠NOP = 44°

STA: MI 9-12.A1.2.1 61. ANS:

hypothesis: tomorrow is Friday, conclusion: today is Thursday

STA: MI 9-12.L4.3.1 62. ANS:

The life she saves may be her own.

STA: MI 9-12.L4.1.1 | MI 9-12.L4.1.3 | MI 9-12.L4.3.3 63. ANS:

2

STA: MI 9-12.A1.2.1 | MI 9-12.G1.1.1

ID: A

4

64. ANS: 50°. Since ∠2 and ∠3 form a linear pair, they are supplementary and the sum of their measures is 180°. So, m∠2 = 180° – 140° = 40°. Since ∠1 and ∠2 are complementary, the sum of their measures is 90°. So, m∠1 = 50°.

STA: MI 9-12.L1.1.3 | MI 9-12.L1.1.4 | MI 9-12.L1.3.1 | MI 9-12.A1.2.4 | MI 9-12.A1.2.5 | MI 9-12.A1.2.6 | MI 9-12.A1.2.7 | MI 9-12.A1.2.8 | MI 9-12.G1.1.1 | MI 9-12.G1.1.2

65. ANS: False; sample counterexample: 6

STA: MI 9-12.L4.1.3 | MI 9-12.L4.2.1 | MI 9-12.L4.2.4 | MI 9-12.L4.3.2 66. ANS:

66°, 64°, 50° (x = 33)

STA: MI 9-12.G1.2.1 | MI 9-12.G1.2.2 67. ANS:

x = 82

STA: MI 9-12.G1.2.1 | MI 9-12.G1.2.2 68. ANS:

A right triangle

STA: MI 9-12.G1.2.5 | MI 9-12.G2.3.1 69. ANS:

12

STA: MI 9-12.G1.3.1 | MI 9-12.G2.3.1 | MI 9-12.G2.3.2 70. ANS:

AB = 21, BC = 35

STA: MI 9-12.A1.2.1 | MI 9-12.G1.1.5 71. ANS:

Since AB = CD =3 10 and BC = AD = 8, ABCD is a parallelogram.

STA: MI 9-12.A1.2.9 | MI 9-12.G1.1.5 | MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3 | MI 9-12.G2.3.4

72. ANS: (–7, 9)

STA: MI 9-12.A1.2.9 | MI 9-12.G1.1.5 | MI 9-12.G1.4.2

ID: A

5

73. ANS: ABCD is a parallelogram. Since ΔABC ≅ ΔCDA and corresponding parts of congruent triangles are congruent, ∠BAC ≅ ∠DCA and∠BCA ≅ ∠DAC. Therefore, AB Ä CD and AD Ä CB and ABCD is a parallelogram.ORSince ΔABC ≅ ΔCDA and corresponding parts of congruent triangles are congruent, AB ≅ CD and AD ≅ CB. Since both pairs of opposite sides are congruent, ABCD is a parallelogram.

STA: MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3 | MI 9-12.G2.3.2 74. ANS:

DC, opposite sides of a parallelogram are ≅.

STA: MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3 75. ANS:

yes

STA: MI 9-12.L4.2.1 76. ANS:

hypothesis: today is Tuesday, conclusion: yesterday was Monday

STA: MI 9-12.L4.3.1 77. ANS:

170 ≈ 13.0

STA: MI 9-12.A1.2.9 | MI 9-12.G1.1.5 | MI 9-12.G1.4.2 | MI 9-12.G2.3.4 78. ANS:

c + e2

, d + b2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

79. ANS: The angle measures 74° and the supplement measures 106°.

80. ANS: CB

81. ANS: a. 4x – 2 = x + 13

b. x = 5. 4x – 2 = x + 13. 4x = x + 15, Addition Property of Equality; 3x = 15, Subtraction Property of Equality; x = 5, Division Property of Equality.

c. m∠RQT = 36. If x = 5, then m∠RQS = 4(5) – 2 = 18 and m∠SQT = 5 + 13 = 18. m∠RQT = m∠RQS + m∠SQT = 18 + 18 = 36.

STA: MI 9-12.L1.1.1 | MI 9-12.L1.1.3 | MI 9-12.A1.2.3 | MI 9-12.A1.2.4 | MI 9-12.A1.2.5 | MI 9-12.A1.2.6 | MI 9-12.A1.2.8

ID: A

6

82. ANS: yes

STA: MI 9-12.L4.2.1 83. ANS:

False 84. ANS:

∠1 or∠3

STA: MI 9-12.G1.1.1 85. ANS:

True

STA: MI 9-12.L4.1.3 | MI 9-12.L4.2.1 | MI 9-12.L4.2.4 | MI 9-12.L4.3.2 86. ANS:

No 87. ANS:

(-9, 5)

STA: MI 9-12.A1.2.9 | MI 9-12.G1.1.5 | MI 9-12.G1.4.2 88. ANS:

The angle measures 79° and the supplement measures 101°. 89. ANS:

27

STA: MI 9-12.G1.4.1 | MI 9-12.G1.4.2 | MI 9-12.G1.4.3 90. ANS:

34

STA: MI 9-12.L1.1.6 | MI 9-12.G1.2.3 | MI 9-12.G1.2.5 | MI 9-12.G1.3.1 91. ANS:

125

STA: MI 9-12.L1.1.6 | MI 9-12.G1.2.3 | MI 9-12.G1.2.5 | MI 9-12.G1.3.1 92. ANS:

AAS

STA: MI 9-12.G2.3.1 | MI 9-12.G2.3.2 93. ANS:

Yes, enough information is given to show ABCD is an isosceles trapezoid. Since ∠CBD ≅ ∠BDA, BC Ä AD. ∠BAC and ∠DCA are not congruent, so BA is not parallel to CD. The legs of trapezoid ABCD

are congruent because BA ≅ CD. Since BC Ä AD and BA ≅ CD, by definition of isosceles trapezoid, ABCD is an isosceles trapezoid.

STA: MI 9-12.G1.4.1 | MI 9-12.G1.4.2

ID: A

7

94. ANS: SAS

STA: MI 9-12.G2.3.1 | MI 9-12.G2.3.2 95. ANS:

Isosceles. ΔTRI ≅ ΔANG., so TR ≅ AN. Then, since ∠T ≅ ∠G, RI ≅ AN by the Converse of the Isosceles Triangle Theorem. So, TR ≅ IR since congruence of segments is transitive. Therefore, ΔABC is isosceles.

STA: MI 9-12.L1.1.3 | MI 9-12.A1.2.4 | MI 9-12.A1.2.5 | MI 9-12.A1.2.6 | MI 9-12.A1.2.7 | MI 9-12.A1.2.8 | MI 9-12.G1.2.2

96. ANS: ASA Congruence Postulate. Since HK and JL are angle bisectors, ∠HLJ ≅ ∠KLJ and ∠HJL ≅ ∠KJL. Since congruence of segments is reflexive, JL ≅ JL. Since you know that 2 pairs of angles and the included Side are congruent, you can use the ASA Congruence Postulate to prove the triangles are congruent.

STA: MI 9-12.G1.1.1 | MI 9-12.G1.4.2 | MI 9-12.G2.3.1 | MI 9-12.G2.3.2 97. ANS:

c and d

STA: MI 9-12.G1.1.2 98. ANS:

c and d

STA: MI 9-12.G1.1.2 99. ANS:

a. See diagram below.b. Yes, because each has a length of 5.c. No. Sample answer: WY ≠ XZ because WY = 8 and XZ = 6.

ID: A

8

OTHER

100. ANS: 1. ABCD is a rhombus. 1. Given

2. ABCD is a parallelogram. 2. Definition of a rhombus

3. AB ≅ CD;BC ≅ AD 3. Opposite sides of a parallelogram are congruent.

4. AC ≅ AC 4. Reflexive Property

5. ΔACB ≅ ΔCAD 5. SSSCongruence Postulate

STA: MI 9-12.G1.4.2 | MI 9-12.G2.3.2 101. ANS:

Statements Reasons

1. ED⊥EC 1. Given

2. ∠CED is a rt ∠ 2. If 2 segments are⊥, they form rt ∠s.

3. BD⊥BC 3. Given

4. ∠DBC is a rt ∠ 4. If 2 segments are⊥, they form rt ∠s.

5. ED ≅ BC 5. Given

6. DC ≅ CD 6. Reflexive

7. ΔCED ≅ ΔDBC 7. HL Congruence Theorem

STA: MI 9-12.G1.4.2 | MI 9-12.G2.3.2 102. ANS:

1. ΔABF ≅ ΔDEC 1. Given

2. BF ≅ EC 2. Corresponding Parts of ≅ Δ are ≅.

3. FB Ä EC 3. Given

4. BCEF is a parallelogram. 4. If 1 pair of opposite sides are and ≅ ,

then the quadrilateral is a parallelogram.

STA: MI 9-12.G1.4.2 | MI 9-12.G2.3.2 103. ANS:

Sample answer: Given: ∠3 ≅ ∠2; Prove: ∠4 and ∠5 are supplementaryFrom the given we know that ∠3 ≅ ∠2. Since ∠2 and ∠5 are vertical angles, they are congruent. If ∠3 ≅ ∠2 and ∠2 ≅ ∠5, then ∠3 ≅ ∠5 by the Transitive Property. By the definition of linear pair, ∠4 and ∠3 are a linear pair and therefore are supplementary. Since ∠3 ≅ ∠5,∠4 and ∠5 are supplementary.

STA: MI 9-12.G1.4.2

ID: A

9

104. ANS: Statements Reasons

1. AE Ä DC; AB ≅ DB 1. Given

2. ∠A ≅ ∠D 2. If 2 parallel lines are intersected by

a transversal, then alternate interior

angles are congruent.

3. ∠ABE ≅ ∠DBC 3. Vertical angles are congruent.

4. ΔABE ≅ ΔDBC 4. ASA Postulate 105. ANS:

1. VU ≅ ST and SV ≅ TU 1. Given

2. STUV is a parallelogram. 2. If both pairs of opp. sides of a quad.

are ≅ , then the quad. is a parallelogram.

3. VX =XT 3. The diagonals of a

parallelogram bisect each other.

STA: MI 9-12.G1.4.2 | MI 9-12.G2.3.2 106. ANS:

Statement Reason

m∠1 = m∠3 Given

m∠1 +m∠2 = m∠3 +m∠2 Addition property of equality

m∠1 +m∠2 = m∠AFC, m∠3 +m∠2 = m∠DFB Angle addition postulate

m∠AFC = m∠DFB Substitution property of equality 107. ANS:

1. BD is the median to AC, AB ≅ BC 1. Given

2. AD ≅ DC 2. Definition of a median

3. BD ≅ BD 3. Reflexive

4. ΔADB ≅ ΔCDB 4. SSS

5.∠CBD ≅ ∠ABD 5. Corresponding parts of ≅ Δs are ≅

STA: MI 9-12.G1.4.2 | MI 9-12.G2.3.2

ID: A

10

108. ANS: Statements Reasons

ΔABC is an equilateral triangle Given

AB ≅ CB Definition of equilateral

D is the midpoint of AC Given

AD ≅ CD Definition of midpoint

BD ≅ BD Reflexive Property of Congruence

ΔABD ≅ ΔCBD SSSCongruence Postulate

STA: MI 9-12.A1.2.3 | MI 9-12.A1.2.4 | MI 9-12.A1.2.5 | MI 9-12.A1.2.6 | MI 9-12.A1.2.8 | MI 9-12.G1.1.3 | MI 9-12.G1.1.5 | MI 9-12.G2.3.1 | MI 9-12.G2.3.2

109. ANS: Statement Reason

1. PR = 12

PT 1. Given

2. 2PR =PT 2. Multiplication property of equality

3. PR + PR =PT 3. Distributive property

4. PT =PR +RT 4. Segment Addition postulate

5. PR +PR =PR +RT 5. Transitive property of equality

6. PR =RT 6. Subtraction property of equality

7. R is the midpoint of PT 7. Definition of midpoint

STA: MI 9-12.G1.4.2 | MI 9-12.G2.3.2