Logic and ReasoningInductive ReasoningClass WorkMake a conjecture about the missing term in the sequence based on the given numbers.

1. 12, 18, 24, 30, ?2. 5, 10, 20, 40, 80,?3. 24, -12, 6, -3, ?4. -40, -30,-20, -10, ?5. ?, 4, 12, 20, 28, 36

Make a conjecture based on the given statement.6. Segments AB∧ACare perpendicular.7. C is the midpoint of XY8. SQUA is a square9. TRI is a triangle10. A is four from B on a number line, B is at 311. x=4

HomeworkMake a conjecture about the missing term in the sequence based on the given numbers.

12. 8 , 24, ?, 216, 64813. 30, 21, 12, 3, ?14. 20,-4,1, -.25, ?15. -25, ?, 5, 20, 3516. ?, 4, 12, 36, 108, 324

Make a conjecture based on the given statement.17. Segments AB∧CDare parallel18. C is the center of Circle C and P is on circle C19. RECT is a rectangle20. TRI is an equilateral triangle21. A is six from B on a number line, B is at 722. xy=14 and x=-7

LogicClass WorkWhat is the validity of the following statements? If false, state a counterexample.

23. The square root of a positive is a positive.24. Tomorrow is the start of a new month because today is the 30th.25. Gold weighs more than feathers.

Negate the following statement. What is the validity of the negation? 26. 2 + 2 = 627. Albany is the capitol of New York.28. A square has 4 sides of the same length

What is the intersection of p and q? Draw a Venn diagram. State the members of p or q and

~p andq.29. p: multiples of 2 between 1 and 20; q: multiples of 3 between 1 and 2030. p: days of the week; q: usual days of the school year that there is no school 31. p: squares; q: quadrilaterals

Create a truth table for each statement.32. p∪q33. p∩q34. p∪ (q∩r )

HomeworkWhat is the validity of the following statements? If false, state a counterexample.

35. The square root of a number is less than the number.36. Tomorrow is the end of the month because today is the 30th.37. Dallas is the capitol of Texas.

Negate the following statement. What is the validity of the negation? 38. 2 + 2 = 439. Trenton is the capitol of New Jersey.40. A triangle has 3 sides of the same length

What is the intersection of p and q? Draw a Venn diagram. State the members of p or q and ~p and q.

41. p: multiples of 2 between 1 and 20; q: multiples of 4 between 1 and 2042. p: winter months; q: summer months 43. p: even numbers; q: 1,2,3,4,5,6,7,8,9,10

Create a truth table for each statement.44. p∩q45. p∪ q46. p∩ ( q∪ r )

If-Then StatementsClass WorkIdentify the hypothesis with 1 line and the conclusion with 2 lines.

47. If today is Tuesday, then tomorrow is Wednesday.48. If it rains today, then I’ll need an umbrella.49. If a quadrilateral is a square, then it has 4 equal sides.50. If x squared is 9, then x is three.51. XA=XB, if x is the midpoint of AB .

State the converse, inverse, and the contrapositive of the following conditional.52. If today is Tuesday, then tomorrow is Wednesday.53. If it rains today, then I’ll need an umbrella.54. If a quadrilateral is a square, then it has 4 equal sides.55. If x squared is 9, then x is three.56. XA=XB, if x is the midpoint of AB .

State the validity of the following conditional. State the converse, inverse, and the contrapositive of the following conditional and the state the validity of each.

57. If a figure is a rectangle, then it has 4 sides.

HomeworkIdentify the hypothesis with 1 line and the conclusion with 2 lines.

58. If I do my homework, then I can go to the movies.59. If I study my notes for an hour, then I’ll improve my test score.60. If triangle is isosceles, then it has at least 2 sides equal.61. If a number is squared, then the result is positive.62. 4x+7=27, if x=5.

State the converse, inverse, and the contrapositive of the following conditional.63. If I do my homework, then I can go to the movies.64. If I do not skip homework problems, then I’ll improve my test score.65. If triangle is isosceles, then it has at least 2 sides equal.66. If a number is squared, then the product is positive.67. 4x+7=27, if x=5.

State the validity of the following conditional. State the converse, inverse, and the contrapositive of the following conditional and the state the validity of each.

68. If two angles are a linear pair, then the two angles are supplemental.

Deductive ReasoningClass WorkMake a conclusion using the Law of Detachment.

69. If someone runs a 4 minute mile at the track meet, then they will win.Bob can run a 4 minute mile.

70. If you plant geraniums, then you will have blooms all summer long.I planted geraniums.

71. If a quadrilateral is a square, then it will have 4 right anglesSQUA is a square.

Decide if the conclusion can be reached using the Law of Detachment.72. If today it rains, then tomorrow it will be sunny.

It is sunny today.Conclusion: It rained yesterday.

73. If you smile, then the whole world smiles with you.John smiles.Conclusion: The whole world smiles with John.

74. If a natural number is multiplied by four, then the product is greater than the number.

½ is multiplied by 4.Conclusion: The product of 4 and ½ is greater than 1/2.

Make a conclusion using the Law of Syllogism.75. If I work hard in math, then I’ll get a good grade.

If I get a good grade, then I will go to a good college.

76. You will get 12 doughnuts, if you by a dozen.If you have 12 doughnuts, then you can share them with friends.

77. If 2 lines are perpendicular, then 4 right angles are formed.If you have 4 right angles, then they are all congruent.

Decide if the conclusion can be reached using the Law of Syllogism.78. If a number is a natural number, then it is real.

If a number is an integer, then it is real.Conclusion: Natural numbers are integers.

79. If x = 4, then x2=16.If x2 = 16, then (x2)2 = 256.Conclusion: If x=4, then (x2)2 = 256.

80. If zigs are zogs, then zogs are zags.If zags are zegs, then zegs are zugs.Conclusion: If zigs are zogs, then zegs are zugs.

HomeworkMake a conclusion using the Law of Detachment.

81. If Tim passes his final, then he will pass for the year.Tim passed his final.

82. If you remember to say please and thank you, then you are polite.Peggy always remembers to say please and thank you.

83. If a line passes through the center of a circle, then it contains a diameter.AB contains P, the center of circle P.

Decide if the conclusion can be reached using the Law of Detachment.84. If today it rains, then the game will be cancelled.

The game was cancelled.Conclusion: It rained today.

85. If x=4, then x2=16.x= -4.Conclusion: x2=16.

86. If a two rays share an endpoint, then they form an angle.EF∧EG share an endpoint.Conclusion:EF∧ EG form an angle.

Make a conclusion using the Law of Syllogism.87. If today is Friday, then tomorrow is Saturday.

If tomorrow is Saturday, then yesterday was Thursday.88. You can buy lunch, if you have $5.

If you buy lunch, then you don’t have to bring lunch.89. If an angle is acute, then the angle is less than 90°.

If you bisect a right angle, then you have an acute angle .Decide if the conclusion can be reached using the Law of Syllogism.

90. If a number is a natural number, then it is an integer.If a number is an integer, then it is real.Conclusion: If 3 is a natural number, then 3 is a real.

91. If a triangle has 2 equal sides, then it isosceles.If a triangle is isosceles, then it has 2 congruent angles.Conclusion: If a triangle has 2 equal sides, then it has 2 congruent angles.

92. If zigs are zogs, then zogs are zugs.If zags are zigs, then zigs are zogs.Conclusion: If zags are zigs, then zogs are zugs.

Intro to ProofsClass WorkProve the following by creating a t-chart.

93. Given: M is the midpoint of AVProve: AM ≅MV

94. Given: XB ≅ BYProve: B is the midpoint of XY

95. Given: RECT is a rectangleProve: ℜ≅CT

96. Write a paragraph proof for #93.HomeworkProve the following by creating a t-chart.

97. Given: M is the midpoint of ANProve: AM=AN

98. Given: XB ≅ BY ; BY ≅ YCProve: XB≅YC

99. Given: SQUA is a squareProve: SQ | QU

100. Write a paragraph proof for #99.

Algebraic ProofsClass WorkGiven the first statement what reason justifies the second statement?

101. 1) 5x + 7 = 19 Given2) 5x = 12

102. 1) 4(x-5)=20 Given2) 4x – 20=20

103. 1) x4=21 Given

2) x=84104. 1) a=b; 4a+5b=10 Given

2) 4(b) +5b=10105. 1) 11=x Given

2) x=11Prove the following by creating a t-chart.

106. Given: 3(x+11)=18 Prove: x= -5

107. Given: 4 x+96 =x+5 Prove: x= -10.5

108. Given: 10x -3(2x -4)=20 Prove: x=2109. Write a paragraph proof for 106.

HomeworkGiven the first statement what reason justifies the second statement?

110. 1) 3x -8 = 20 Given2) 3x = 28

111. 1) 4(x-5)=20 Given2) x-5 = 5

112. 1) 8x+9=37 Given2) 8x=28

113. 1) 5a=b+9; b+9=10 Given2) 5a=10

114. 1) 4 x+23

=3 x−65 Given

2) 5(4x+2)=3(3x-6)Prove the following by creating a t-chart.

115. Given: 4x – 3(x-5)=18 Prove: x= 3

116. Given: 3x+62 =

2x−13 Prove: x= -4

117. Given: 10x – 4(2x)+6=20 Prove: x=7118. Write a paragraph proof for 116.

Proofs with Segments and AnglesClass WorkFind x and AN.

119. N is between A and B. AN=2x, NB=4x, and AB= 24120. N is between A and B. AB = 5x-9, BN= 3x+2, and NA= x-2121. N is the midpoint AN= 2x+y, BN= x+3y, AB=20

Find x and m∠ ABX .122. BX lies on the interior of ∠ ABC. m∠ ABC=80, m∠ ABX=2 x, and

m∠CBX=3x.123. BX lies on the interior of ∠ ABC. m∠ ABC=7x-20, m∠ ABX=3 x+2, and

m∠CBX=x+6.124. BX bisects ∠ ABC. m∠ ABC=52, m∠ ABX=2 x+3 y , and m∠CBX=3x

– 2y.Prove the following by creating a t-chart.

125. Given: AB=XY and BC=YZProve: AC=XZ

126. Given: AB=CDM is the midpoint of AB

N is the midpoint of CD

Prove: AM ≅CN127. Given: ∠ ABC≅∠XYZ ;BE bisects∠ABC ;YF bisects∠XYZ

Prove: ∠ ABE≅∠ XYF128. Given: ∠ ABF≅∠MNG;∠FBC ≅∠GNP

Prove: ∠ ABC≅∠MNP129. Write a paragraph proof for 128

HomeworkFind x and AN.

130. N is between A and B. AN=3x, NB=5x-6, and AB= 26131. N is between A and B. AB = 5x, BN= 3x-6, and NA= x+12132. N is the midpoint AN= 6x+2y, BN= 5x+6y, AB=104

Find x and m∠ ABX .133. BX lies on the interior of ∠ ABC. m∠ ABC=60, m∠ ABX=2 x−6, and

m∠CBX=4x.134. BX lies on the interior of ∠ ABC. m∠ ABC=3x-10, m∠ ABX=x+12, and

m∠CBX=x-2.135. BX bisects ∠ ABC. m∠ ABC=90, m∠ ABX=4 x+2 y, and m∠CBX=5x

– 2y.Prove the following by creating a t-chart.

136. Given: AB=XY and AC=XZProve: BC=YZ

137. Given: AM=CNM is the midpoint of AB

N is the midpoint of CDProve: MB≅ ND

138. Given: ∠ ABE≅∠ XYF ;BE bisects∠ ABC ;YF bise cts∠XYZProve: ∠ ABC≅∠XYZ

139. Given: ∠ ABF≅∠MNG;∠FBC ≅∠GNPProve: ∠ ABC≅∠MNP

140. Write a paragraph proof for 137

Multiple Choice1. Given: x2>0, Conjecture: x>0. Is the conjecture True of False, if false give a counter

example.a. True b. False, x= -2 c. False, x=1/2 d. False, x=0

2. What is the inverse of: If x=3, then 2x=6a. If 2x≠6, then x=3 b. If 2x≠6, then x≠3 c. If x≠3, then 2x≠6 d. If 2x=6, then x=3

3. If gold is pure then its 24 karat. Jen’s ring is pure gold. We can conclude that her ring is 24 karat. This is an example ofa. Contrapositive b. Law of Syllogism c. Law of Detachment d. None of these

4. What property justifies: If 3x-2=8, then 3x=10.

a. Substitution b. Addition c. Division d. Transitive

5. What property justifies: If 4 x−56 =8, then 4x-5=48.

a. Distribution b. Addition c. Multiplication d. Transitive6. D is between S and T. DS= 4x+8, ST=7x , and DT=2x-3. Find DT

a. 5 b. 7 c. 28 d. 357. AX lies on the interior of ∠MAD, m∠MAX=22, m∠ XAD=5x+10, and

m∠M AD=15x+2. Find m∠ XADa. .5 b. 3 c. 11.4 d. 25

8. What is the reason that allows statement 2 to be made?∠ ABCis a¿angle Givenm∠ ABC=90 ?

a. Definition of perpendicular b. Definition of a right angle c. Addition Property d. Definition of Complementary

9. What is the reason that allows statement 2 to be made?Bis between A∧C GivenAB+BC=AC ?

a. Addition Property b. Definition of a Midpoint

c. Betweenness Theoremd. Segment Bisector

10. When is p∪q a true statement?a. when p is true and q is trueb. when p is true or q is true c. when p is false and q is trued. when p is false or q is true

11. The contrapositive of: If toady is Monday, then tomorrow is Tuesday, isa. If today is Tuesday, then yesterday was Monday.b. If tomorrow isn’t Tuesday, then yesterday wasn’t Monday.c. If tomorrow isn’t Tuesday, then today isn’t Monday.d. If today isn’t Monday, then tomorrow isn’t Tuesday.

12. What is the hypotheses ofIt’s going to be a great day, if you get up on the right side of the bed.

a. It’s going to be a great dayb. You get out on the right side of the bedc. You got a good night sleepd. Today is not a great day

Open Ended1. a. Create a truth table for: p∪(q∩ r)

b. What is the validity of p is true, q is false, and r is true?c. How can a truth table be used to show two statements are equivalent?

2. Create a two-column proof for the solution of 2( 5 x−34 )=113. Refer to the statement: All quadrilaterals are rectangles.

a. Write a conditional based on this statement.b. Is the conditional in part a true or false, if false give a counter example.c. Write the contrapositive of the conditional from part a.

Answers1. Add 6; 362. Multiply by 2; 1603. Div. by -2; 1.54. Add 10; 05. Add 8; -46. Make a right angle7. Xc=cy8. All sides are equal9. Has 3 sides10. A is -1 or 711. X2=1612. Mult 3; 7213. Subtract 9; -614. Divide by -4; .062515. Add 15: -1016. Mult 3; 4/317. AB and CD have no points in common18. CP is a ridus19. RE ≥ CT20. TR=RI =TI21. B is 1 or 1322. Y=-223. True24. False, it could be October 30th

25. False, it depends how many pounds of each

26. 2+2 ≠6 True27. Albany is not the capital of new York.

False28. A Square does not have four sides of

the same length. False

29. P^q: {6,12,18} ; p U q {2,3,4,6,8,9,10,12,14,15,16,18,20} ; -p ^q {3,9,15}

[Type a quote from the document or the summary of an interesting point. You can position the text box anywhere in the document. Use the Text Box Tools tab to change the formatting of the pull quote text box.]

(middle= 6, 12,8 for diagram above)30. P^q { SA SU}; p u q { SA SU MO TU WE

TH FR}; -p ^q { mon tues wed thur fri}

2 10 20 4 14 8 16 3 9 15

S A SU

Mon, Tues, Wed, Thurs, Fri

31. P ^q { 14}; p u q{2,5,6,8,.10,11,14,17,18,20}; _ p ^q { 5,8,11,17,20}

Middle= 2, 14

P Q P u qT T TT F TF T TF F F

32.33.

P P Q P^qT F T FT F F FF T T TF T F F

P Q R Q^R P^ / Q^R

T T T T TT T F F FT F T F FT F F F FF T T T FF T F F FF F T F FF F F F f

34.

35. False √ 14=1 /236. False, today could be sept 30th

37. False, austin is the capital

38. 2+2 ≠4 false39. Trenton is not the capital of NJ, false40. A triangle does not have 3 sides the

same length; false41. P^q {4,8,12,16,20}; p u q

{2,4,6,8,18,20}; {2,6,10,14,18)

42. P ^q: none; p u q: {dec,jan, feb, jue, july aug}; ~p ^ q; {June july aug}

P Q

43. P^q: {2,4,8,10}; p u q: {1,2,3,4,5,6,7,8,9,10,12,14,16,18,20} ~p ^ q {1,3,5,7,9}

Middle= 2, 4,6, 8 10

P Q P^qT T T

2 6 10 18

5 8 11 17 20

12 14 16 18

20

1 3 5 7 9

4 8 12 16 20

P q 2 6 10 14 18

Dec, Jan, Feb

June, July, Aug

T F FF T FF F F

44.

P Q ~P ~Q ~P U q

T T F F FT F F T TF T T F TF F T T T

45.

P Q R ~Q ~R ~Q u ~R

P ^( ~QU ~R)

T T T F F F FT T F F T T TT F T T F T TT F F T T T TF T T F F F FF T F F T T FF F T T F T FF F F T T T F

46.47. If today is Tuesday, then tomorrow is

Wednesday.48. If it rains today, then I’ll need an

umbrella.49. If a quadrilaterial is a square, then it has

four equal sides50. If x squared is 9, then x is three.51. XA=XB , if x is the midpoint of AB. 52. Conv: If tomorrow is wed, then today is

tues; inv: If today is not tues, then tomorrow isn’t wed; Cont: If tomorrow isn’t wed, then today isn’t tues.

53. Conv: If I’ll need an umbrella, then it rains today; Inv: If it doesn’t rain today, then I won’t need an umbrella; Cont: If I don’t need an umbrella, then it didn’t rain today

54. Con: If it has four sides, then a quadrilateral is a square; Inv: If a quad is not a square, then it doesn’t have four sides; Cont: If a quad has four equal sides, then it is not a square

55. Con: If x=3, then x2=9; Inv: if x2=9, then x≠3; Cont: if x≠3, then x2≠9

56. Con: If XA=XB, then x is the midpt of AB; Inv: If x is not the midpt of AB, then XA ≠XB; Cont: If XA ≠XB, then x is ot the midpt of AB

57. Statement is true; Conv: If a figure has four sides, then it is a rectangle; fls; INV: If a figure is not a rect, then it doesn’t have four sides; false; Cont: If a figure doesn’t have four sides, then it is not a rect; true

58. If I do my homework , then I can go to the movies.

59. If I study my notes for an hour , then I’ll improve my test score.

60. If a triangle is isosceles , then it has at least two sides equal.

61. If a number is squared , then the result is positive.

62. 4x+7=27 , if x=5. 63. CON: if I can go to the movies, then I do

my homework; INV: if I don’t do my homework, then I cant go to the movies; CONTR: if I cant go to the movies, then I didn’t do my homework.

64. CON: if I improve test scores, then I didn’t skip homework problems; INV: if I skip homework problems, then I wont improve my test scores; CONTR: if I don’t improve test scores, then I skipped homework problems.

65. CON: if a triangle has at least 2 sides equal, then it is isosceles; INV: if a triangle is not isosceles, then it doesn’t have at least two sides.; CONTR: If a

triangle does not have at least two sides equal, then it is not isosceles.

66. CON: if the product is positive, then a number is squared; INV: if a number isn’t squared, then the product is not positive. CONTR: if the product isn’t positive, then a number isn’t squared.

67. Conv: if 4x+7=27, then x=5’ Inv: If x≠5, then 4x+7 ≠27. Contr: If 4x+7≠27, then x≠5

68. Statement is true; conv: if two angles are supplemental, then the angles are a linear pair (false); Inv: if two angles are not a linear pair, then they are not supplemental (false); Contr: If two angles are not supplemental, then they are not a linear pair (true)

69. Bob will win70. I will have blooms all summer long71. Square has four right angles72. No: p→q +q is true73. Yes74. No75. If I work hard in math then I will go to a

good college.76. Not possible77. If two lines are perpendicular, then four

angles are congruent.78. No79. Yes80. No81. Tim will pass for the year82. Peggy is polite83. AB contains a diameter84. No85. No86. Yes87. If today is Friday then yesterday was

Thursday88. If you have five dollars, then you don’t

have to bring lunch.

89. If you bisect an angle then the angle is less than 90 degrees.

90. Yes91. Yes92. Yes93.

Statement ReasonN is midpoint of AU

Given

AM≅MU Def of midptAM ≅MN Def of

congruence94.

Statement ReasonXB ≅BY GivenXB = BY Def of congruenceB is midpt of XY Def of midpt

95.

Statement ReasonRECT is a rectangle GivenRE ≅CT Prop of rectangle

96. Dt is given. N is the midpoint of AV. AM ≅MV by definition of a midpoint. Using the definition of congruent AM = MV.

Statement ReasonM is midpoint o AN

Given

AM = AN Def of midpoint 97.

Statement ReasonXB ≅BY BY ≅YC GivenXB ≅ YC Transitive

property98.

Statement ReasonSQUA is a square Given<Q is a right angle Prop of a squareSQ is perpendicular to QU

Def of perpendicular

99. 100. SQUA is given to be a square. A

property of a square is that it has four right angles, therefore <Q is a right angle. SQ is perpendicular to QU by the definition of perpendicular.

101. Addition (subtraction) property of equality

102. Distribution103. Multiplication property of

equality104. substitution105. Symmetry106.

Statement Reason3(x+11) =18 Given3x+33=18 Distribution

3x=-15 Add prop of eq.X=-5 Division prop of

eq.107.

Statement Reason4 x+96 =x+5

Given

4x+9=6x+30 Mult prop of eq.

-21=2x Add prop of eq.-10.5 =x Mult (division)

propX=-10.5 symmetric

108.

Statement Reason10x-3(2x-4)=20 Given

10x-6x+12=20 Distribution4x+12=20 Addition4x=8 Addition

(subtraction) prop of eq

X=2 Multiplication (division) prop of eq

109. Given 3(x+11)=18, use distribution property to get 3x+33=18. 3x=-15, results from using addition property of equality. The solution of x=-5 is found by applying multiplication property.

110. Addition property111. Multiplication property112. Addition property113. Transitive property114. Multiplication property115.

Statement Reason4x+3(x-5)=18 Given4x-3x+15=18 DistributionX+15=18 AdditionX=-3 Addition prop of

eq

116.

Statement Reason3x+62

=2 x−13

Given

3(2x+6)=2(2x-1) Mult prop of eq9x+18 =4x-2 Distribution prop5x=-20 Addition prop of

eqX=-40 multiplication

117.

Statement Reason10x-4(2x)+6=20 Given10x-8x+6=20 Multiplication

2x+6=20 Addition2x=14 Addition prop of

eqX=7 Multiplication prop

118. 3x+62

=2 x−13 is given. Cross multiply

to get 3(3x+6) =2(2x-7). Distribution leads to 9x+18=4x+2. 5x=-20 is arrived at by using addition prop of eq to add -4x to both sides and -18 to both sides. Using multiplication property of equality, x=-4.

119. X=4, AN =8120. X=9, AN=7121. X=4 AN =10122. X=16, m<ABX=32123. X=7, m<ABX =23124. X=10, m<ABX =26

Statement ReasonAB=x4 and BC=42 GivenAB+BC =x4+47 Addition prop of

eqAB+BC=AC AdditionX4+47=x7 ADDAC=x7 substitution

125. 126.

Statement ReasonAB=CDM is midpt of ABN is midpt of CD

Given

AM=MB, CN=ND Def of midptAM+MB =AB, CN+ND=CD

Segment addition

AM+MB = CN+ND SubstitutionAM+AM =CN +CN Substation2AM=@CN AdditionAM=CN Mult prop of eq

Statement Reason<ABC ≅ <XYZ GivenM<ABC + m<EBC =m<ABC

Angle addition

M<ABC = M<EBC = m<XYF + m<FYZ

Substitution

BE bisects <ABC 4f bisects <XYZ

Given

M<ABC = m<EBC M<XYZ = m<FYZ

Def of bisects

M<ABC =m<ABE = m<XYZ +m<XYZ

Substit five into 3

2m<ABE = 2m<XYZ

Addition

M<ABE = m<XYF Mult prop<ABE ≅<XYF Def of congruent

127.

Statement Reason<ABF ≅<MNG;<FBC ≅<GNP

Given

M<ABF = m<MNGM<FBC= m<GNP

Def og congruent

M<ABF + m<FBC =m<MNG + m<GNP

Add prop

,<ABF = m<FBC = m<ABC

Angle add

M<ABC = m<MNP Substitution<ABC ≅<MNP Def of congruent

128. 129. 130. X=4 AN=12131. X=6, AN=18132. X=8 AN=52133. X=11 m<ABX =16134. X=20 m<ABX =32135. X=10 m<ABS =45

Statement ReasonAB=XY; AC=YZ GivenAC=AB +BCXZ=XY+YZ

Seg addition

AB+BC =XY +YZ SubstitutionBC=YZ Add property of eq

136. ]

Statement ReasonM IS MIDPT OF ABN IS MIDPT OF CD

GIVEN

AB = AM +MBCD=CN+ND

SEG ADDITION

AM=MBCN=ND

DEF OF MIDPT

AM=CN GIVEN2M=2CN MULT PROPAM+AM=CN+CN ADD PROPAM+MB = CN+ND SUBSTAB=CD SUBST

137.

STATEMENT REASONBE BISECTS <ABCYF BISECTS <XYZ

GIVEN

M<ABE = M<EBCM<XYF = M<FYZ

DEF OF BISECTS

M<ABE = M<EBC GIVEN2M<ABE = 2M<EBC

138. 139. 140.

MULTIPLE CHOICE1. B2. C3. C4. B5. C6. B7. D8. B

9. C10. D11. C12. B

OPEN ENDED1. A)

p Q R ~p Q^r ~p U (q^r)

T T T F T TT T F F F FT F T F F FT F F F F FF T T T T TF T F T F TF F T T F TF F F T F T

b) falseC) If true and false for same inputs

2.

Statements Reason

2 (5x−34 =11

Given

5x−32 =11

Distribution

5x-3=22 Mult prop of eq

5x=25 Add prop of eqX=5 Mult prop of

eq

3. A) if a figure is a quadrilateral,

then it is a rectangle.B) False, a trapezoidC) if a figure is not a rectangle, then it is not a quadrilateral