GEM 8 MID-TERM REVIEW FOR WINTER BREAK

Transcription

1 Name: lass: ate: I: GEM 8 MI-TERM REVIEW FOR WINTER REK Multiple hoice Identify the choice that best completes the statement or answers the question. Show all necessary work on rough work paper. Write the answer selected on answer sheet given. omplete the sentence yd =? ft a. 99 c. 87 b. 90 d ,792 cm =? m a c. 5 b. 48 d in.? cm a. 195 c. 196 b. 192 d m? yd a c b d. 9.9 Find the probability. 5. person is randomly selected from a group consisting of 6 republicans, 20 democrats, and 19 independents. Find P(independent). Round to the nearest percent if necessary. a. 73% c. 62% b. 44% d. 42% 6. marble is randomly selected from a bag containing 10 black, 14 white, and 7 clear marbles. Find P(white). Round to the nearest percent if necessary. a. 32% c. 65% b. 45% d. 82% Evaluate the expression. 7. x 7 + y if x = 1 and y = 6. a. 2 c. 2 b. 14 d. 0 1

2 Name: I: 8. 3ab + c if a = 6, b = 2 and c = 6. a. 30 c. 31 b. 26 d. 34 Solve the equation y = x = g < 25 a. 0 c. 1 b. 59 d. 4 a. 5 c. 11 b. 8 d. 4 Solve the inequality. Ï a. Ì Ô g g < 25 ÓÔ Ô Ô Ï b. Ì Ô g g < 24 ÓÔ Ô Ô Ï c. Ì Ô g g < 28 ÓÔ Ô Ô Ï d. Ì Ô g g < 29 ÓÔ Ô Ô 12. 4t 36 Ï a. Ì Ô t t 9 ÓÔ Ô Ô Ï b. Ì Ô t t 10 ÓÔ Ô Ô Ï c. Ì Ô t t 9 ÓÔ Ô Ô Ï d. Ì Ô t t 4 ÓÔ Ô Ô 2

3 Name: I: Find the point on a coordinate plane. 13. Find the ordered pair for point. a. (1, 4) c. ( 1, 4) b. ( 1, 4) d. (1, 4) 14. Name the quadrant in which point (2, 3) is located. a. III c. I b. IV d. II Solve the system of equations x + y = 13 2x + 5y = x + y = 1 a. (4, 5) c. (4, 2) b. (5, 5) d. (5, 4) 3x 6y = 6 a. (3, 2) c. (0, 1) b. (2, 1) d. (0, 1) 3

4 Name: I: Simplify a. 5 3 c. 15 b d a. 37 c b. 2 3 d Refer to Figure 1. Figure Name a line that contains point J. a. c. n b. GF d. p 20. Name the plane containing lines m and p. a. n c. H b. GF d. J 21. What is another name for line n? a. line J c. GF b. d. 22. What is another name for line m? a. line JG c. b. JG d. line J 4

5 Name: I: 23. Name a line that contains point. a. c. K b. m d. 24. Name a point NOT contained in or FG. a. K c. H b. d. 25. Which of these is NOT a way to refer to line? a. J c. J b. m d. line J 26. Name three points that are collinear. a., G, F c. J, G, F b.,, H d. J,, G 27. Name three points that are collinear. a. M, L, R c. Q, L, M b. L, P, T d. R, S, K 5

6 Name: I: 28. Lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b. raw and label a figure for this relationship. a. c. b. d. 29. re points,,, and F coplanar? Explain. a. Yes; they all lie on plane P. b. No; they are not on the same line. c. Yes; they all lie on the same face of the pyramid. d. No; three lie on the same face of the pyramid and the fourth does not. 6

7 Name: I: Refer to Figure 2. Figure Name three collinear points. a., L, c. K,, b., L, d., F, G 31. Where could you add point M on plane L so that,, and M would be collinear? a. anywhere on F c. anywhere on L b. anywhere on L d. anywhere on 32. Name a point that is NOT coplanar with G,, and. a. K c. b. d. F 33. Name four points that are coplanar. a. G,, L, c. L,,, G b., K,, G d. K,,, L 34. Name an intersection of plane GFL and the plane that contains points and. a. line L c. line b. d. plane 35. Which plane(s) contain point K? a. plane G c. plane G, plane b. plane, plane L d. plane 36. Find the value of the variable and LN if M is between L and N. LM = 8a, MN = 7a, LM = 56 a. a = 3.73, LN = c. a = 8, LN = 120 b. a = 7, LN = 105 d. a = 7, LN = 49 7

8 Name: I: In the figure, GK bisects FGH. 37. If m FGK = 7w + 3 and m FGH = 104, find w. a. 7 c. 52 b d. 3.5 In the figure, KJ and KL are opposite rays. 1 2 and KM bisects NKL. 38. Which is NOT true about KM? a. MKJ is acute. b. 3 MKL c. Point M lies in the interior of LKN. d. It is an angle bisector. 39. If JKN is a right angle and m 1 = 4t + 5, what is t? a c b. 10 d. 45 8

9 Name: I: Use the figure to find the angles. 40. Name two acute vertical angles. a. KQL, KQM c. GQI, IQM b. KQL, IQH d. HQL, IQK 41. Name a pair of obtuse adjacent angles. a. KQG, HQM c. GQI, IQM b. GQL, LQJ d. HQG, IQH 42. Name a linear pair. a. KQG, HQM c. GQI, IQM b. GQL, LQJ d. LQG, KQM 43. Name an angle supplementary to MQI. a. IQG c. MQK b. GQL d. IQH 44. Name two obtuse vertical angles. a. KQL, KQM c. GQI, IQM b. KQL, IQH d. HQL, IQK 45. Two angles are supplementary. One angle measures 26 o more than the other. Find the measure of the two angles. a. 77, 103 c. 167, 193 b. 32, 58 d. 76, 104 9

10 Name: I: Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. 46. a. triangle, convex, regular c. triangle, concave, irregular b. triangle, convex, irregular d. quadrilateral, convex, irregular 47. a. quadrilateral, convex, regular c. pentagon, convex, irregular b. quadrilateral, concave, irregular d. quadrilateral, convex, irregular Find the length of each side of the polygon for the given perimeter. 48. P = 72 units. Find the length of each side. a. 9 units, 36 units, 4 units, 23 units b. 8 units, 33 units, 4 units, 21 units c. 9 units, 35 units, 5 units, 23 units d. 10 units, 34 units, 6 units, 22 units 10

11 Name: I: Find the area of the figure. 49. a cm 2 c cm 2 b. 5.4 cm 2 d cm Name the bases of the solid. a. and c. ñ and ñ b. and d. ñ and ñ 51. Name the bases of the prism. a. ΔUWY and ΔVXZ c. UVZY and UVXW b. UVZY and WXZY d. UVXW and WXZY 11

12 Name: I: Name the vertices of the solid. 52. a.,, I, G, E, and K c.,,, and b.,, J, H, F, and L d.,,,, E, F, G, H, I, J, K, and L Make a conjecture about the next item in the sequence , 4, 16, 64, 256 a c b d etermine whether the conjecture is true or false. Give a counterexample for any false conjecture. 54. Given: points,,, and onjecture:,,, and are coplanar. a. False; the four points do not have to be in a straight line. b. True c. False; two points are always coplanar but four are not. d. False; three points are always coplanar but four are not. 55. Given: a concave polygon onjecture: It can be regular or irregular. a. False; to be concave the angles cannot be congruent. b. True c. False; all concave polygons are regular. d. False; a concave polygon has an odd number of sides. 56. Given: Point is in the interior of. onjecture: a. False; m may be obtuse. b. True c. False; just because it is in the interior does not mean it is on the bisecting line. d. False; m + m = Given: m = 10 onjecture: m = 2 a. False; m = 4 c. False; m = 3 b. True d. False; m = 2 12

13 Name: I: 58. Given: points R, S, and T onjecture: R, S, and T are coplanar. a. False; the points do not have to be in a straight line. b. True c. False; the points to not have to form right angles. d. False; one point may not be between the other two. 59. Given:, E are coplanar. onjecture: They are vertical angles. a. False; the angles may be supplementary. b. True c. False; one angle may be in the interior of the other. d. False; the angles may be adjacent. 60. Given: Two angles are supplementary. onjecture: They are both acute angles. a. False; either both are right or they are adjacent. b. True c. False; either both are right or one is obtuse. d. False; they must be vertical angles. 61. Given: F is supplementary to G and G is supplementary to H. onjecture: F is supplementary to H. a. False; they could be right angles. b. False; they could be congruent angles. c. True d. False; they could be vertical angles. 62. Given: onjecture: a. False; the angles are not vertical. b. True c. False; the angles are not complementary. d. False; there is no indication of the measures of the angles. 13

14 Name: I: 63. Given: segments RT and ST; twice the measure of ST is equal to the measure of RT. onjecture: S is the midpoint of segment RT. a. True b. False; point S may not be on RT. c. False; lines do not have midpoints. d. False; ST could be the segment bisector of RT. Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value. p: n isosceles triangle has two congruent sides. q: right angle measures 90 r: Four points are always coplanar. s: decagon has 12 sides. 64. p s a. n isosceles triangle has two congruent sides and a decagon has 12 sides; true. b. n isosceles triangle has two congruent sides or a decagon has 12 sides; false. c. n isosceles triangle has two congruent sides or a decagon has 12 sides; true. d. n isosceles triangle has two congruent sides and a decagon has 12 sides; false. 14

15 Name: I: omplete the truth table. 65. p q r q r q T T T T T F T T F F F F F F 15

16 Name: I: a. p q r q r q T T T F F T T F F F T F T T T T F F T F F T T F F F T F F F F F T T T b. F F F T F p q r q r q T T T F F T T F F F T F T T T T F F T F F T T F F F T F F T F F T T F c. F F F T F p q r q r q T T T F F T T F F F T T T F F T T F T F F F T T T F F F T F F F T T T F F F T F 16

17 Name: I: d. p q r q r q T T T F F T T F F F T F T T T T F F T F F T T F F F T F F F F F T T F F F F T F Write the statement in if-then form. 66. counterexample invalidates a statement. a. If it invalidates the statement, then there is a counterexample. b. If there is a counterexample, then it invalidates the statement. c. If it is true, then there is a counterexample. d. If there is a counterexample, then it is true. 67. Two angles measuring 90 are complementary. a. If two angles measure 90, then two angles measure 90. b. If two angles measure 90, then the angles are complementary. c. If the angles are supplementary, then two angles measure 90. d. If the angles are complementary, then the angles are complementary. Write the converse of the conditional statement. etermine whether the converse is true or false. If it is false, find a counterexample. 68. If you have a dog, then you are a pet owner. a. If you are a pet owner, then you have a dog. True b. dog owner owns a pet. True c. If you are a pet owner, then you have a dog. False; you could own a hamster. d. If you have a dog, then you are a pet owner. True 69. ll Jack Russells are terriers. a. If a dog is a terrier, then it is a Jack Russell. False; it could be a Scottish terrier. b. If it is a Jack Russell, then a dog is a terrier. True c. If a dog is a terrier, then a dog is a terrier. True d. ll Jack Russells are terriers. True 17

18 Name: I: Write the inverse of the conditional statement. etermine whether the inverse is true or false. If it is false, find a counterexample. 70. People who live in Texas live in the United States. a. People who do not live in the United States do not live in Texas. True b. People who do not live in Texas do not live in the United States. False; they could live in Oklahoma. c. People who live in the United States live in Texas. False; they could live in Oklahoma. d. People who do not live in Texas live in the United States. True 71. ll quadrilaterals are four-sided figures. a. ll non-quadrilaterals are four-sided figures. False; a triangle is a non-quadrilateral. b. ll four-sided figures are quadrilaterals. True c. No quadrilaterals are not four-sided figures. True d. No four-sided figures are not quadrilaterals. True 72. n equilateral triangle has three congruent sides. a. non-equilateral triangle has three congruent sides. False; an isosceles triangle has two congruent sides. b. figure that has three non-congruent sides is not an equilateral triangle. True c. non-equilateral triangle does not have three congruent sides. True d. figure with three congruent sides is an equilateral triangle. True 73. ll country names are capitalized words. a. ll capitalized words are country names. False; the first word in the sentence is capitalized. b. ll non-capitalized words are not country names. True c. ll non-country names are capitalized words. False; most of the words in the sentence are non-capitalized words. d. ll non-country names are non-capitalized words. False; the first word in the sentence is capitalized. 74. Independence ay in the United States is July 4. a. July 4 is not Independence ay in the United States. False; it is Independence ay. b. Non-Independence ay in the United States is not July 4. True c. Non-Independence ay in the United States is July 4. False; July 4 is Independence ay in the United States. d. Non-July 4 is not Independence ay in the United States. True Write the contrapositive of the conditional statement. etermine whether the contrapositive is true or false. If it is false, find a counterexample. 75. If you are 16 years old, then you are a teenager. a. If you are not a teenager, then you are not 16 years old. True b. If you are not 16 years old, then you are not a teenager. False; you could be 17 years old. c. If you are not a teenager, then you are 16 years old. True d. If you are a teenager, then you are 16 years old. False; you could be 17 years old. 18

19 Name: I: 76. converse statement is formed by exchanging the hypothesis and conclusion of the conditional. a. non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. True b. statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. False; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. c. non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. False; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. d. statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. True 77. Two angles measuring 180 are supplementary. a. Two angles not measuring 180 are supplementary. True b. More than two angles measuring 180 are non-supplementary. True c. Non-supplementary angles are not two angles measuring 180. True d. Non-supplementary angles are two angles measuring 180. False; supplementary angles must measure If you have a gerbil, then you are a pet owner. a. If you are not a pet owner, then you do not have a gerbil. True b. If you do not have a gerbil, then you are not a pet owner. False; you could have a dog. c. If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets. d. If you are not a gerbil, then you are not a pet owner. True 79. Thanksgiving ay in the United States is November 25. a. If it is not November 25, it is Thanksgiving ay in the United States. True b. If it is not Thanksgiving ay in the United States, it is not November 25. False; Thanksgiving ay could be another date in a different year so November 25 could be not Thanksgiving ay. c. If it is not November 25, it is not Thanksgiving ay in the United States. True d. If it is not November 25, it is not Thanksgiving ay in the United States. False; Thanksgiving ay could be another date in a different year. etermine whether statement (3) follows from statements (1) and (2) by the Law of etachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. 80. (1) You are in ninth grade. (2) People who are in ninth grade floss their teeth regularly. (3) You floss your teeth regularly. a. yes; Law of Syllogism b. invalid c. yes; Law of etachment 19

20 Name: I: In the figure below, points,,, and F lie on plane P. State the postulate that can be used to show each statement is true. 81. and are collinear. a. If two points lie in a plane then the entire line containing those points lies in that plane. b. Through any two points there is exactly one line. c. If two lines intersect then their intersection is exactly one point. d. line contains at least two points. 82. Line contains points and. a. If two lines intersect then their intersection is exactly one point. b. If two points lie in a plane then the entire line containing those points lies in that plane. c. line contains at least two points. d. Through any two points there is exactly one line. Refer to the figure below. 83. Name all planes intersecting plane I. a., G, I, FGH c., GFI, G, GF b., F, HGF d., G, F 20

21 Name: I: 84. Name all segments parallel to GF. a.,, HI c., HI b.,, HI d., 85. Name all segments skew to. a. FI,, F, I c.,, G, H b. FG, GH, HI, FI d. GF, HI, I, F 86. Name all segments parallel to GH. a. G, H, FG, HI c.,, HI b.,, F, I d.,, FI 87. Name all planes intersecting plane HG. a., I, FI, GF c., IH, FIH, HI b., I, FIH, F d., F, FGH, G 88. Name all segments skew to HI. a.,, F, G c.,,, b. FI, GH, I, H d., G, F, FG 89. Name all segments parallel to. a.,, GH, FI c., FG, HI b. I, H, GH, FI d. GH,, FI 90. Name all segments skew to GF. a.,, I, H c.,,, b. FI, GH, I, H d., H, I, HI 91. Name all planes intersecting plane F. a. GH,, FI, IH c. H, GFI, FGH, G b., HG, FI, FIH d. H, F, G, 92. Name all segments parallel to G. a., FG, GH, c. F, I, H b.,, HI, FI d. GH,, FI 21

22 Name: I: 93. line j Identify the sets of lines to which the given line is a transversal. 94. line a a. lines m and n n and o m and o b. lines m and p n and o c. lines i d. lines m and n n and o m and o m and p n and p o and p a. lines c and b f and d c and f c and d b and d b. lines a and b a and c a and d a and f c. lines f and d c and f c and d b and d d. lines c and b f and d etermine whether WX and YZ 95. WÊ Ë 0, 3 Ê Ë 5 Ê Ë 5 Ê ËÁ 1, 2 ˆ a. parallel b. perpendicular c. neither are parallel, perpendicular, or neither. 22

23 Name: I: Write an equation in point-slope form of the line having the given slope that contains the given point. 96. m = 0.8, Ê ËÁ 14.5, 12.8 ˆ a. y 14.5 = 0.8(x 12.8) c. y = 0.8x 1.2 b. y 12.8 = 0.8(x 14.5) d. y = 0.8(x 14.5) Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. a. c Ä d; congruent corresponding angles b. a Ä b; congruent corresponding angles c. c Ä d; congruent alternate interior angles d. a Ä b; congruent alternate interior angles 23

24 Name: I: 98. LHO NKP a. c Ä d; congruent corresponding angles b. a Ä b; congruent corresponding angles c. a Ä b; congruent alternate exterior angles d. c Ä d; congruent alternate exterior angles 24

25 Name: I: onstruct a line perpendicular to m through P. Then find the distance from P to m. 99. Line m contains points Ê Ë Á 3, 1 ˆ and Ê Ë Á1, 1 ˆ. Point P has coordinates Ê ËÁ 5, 2 ˆ. a. c. b. d = 1 d. d = 2 d = 1 d = 5 25

26 Name: I: 100. Line m contains points Ê Ë Á 3, 3 ˆ and Ê Ë Á0, 0 ˆ. Point P has coordinates Ê ËÁ 1, 2 ˆ. a. c. b. d = 2.55 d. d = 2.12 d = 2.02 d = y = 4x + 4 Find the distance between the pair of parallel lines. 4x y = 1 a. d = 1.64 c. d = 1.21 b. d = 1.47 d. d =

27 Name: I: Use a protractor to classify the triangle as acute, equiangular, obtuse, or right a. obtuse c. equiangular and obtuse b. right d. equiangular and acute Find each measure m 1, m 2, m 3 a. m 1 = 135, m 2 = 88, m 3 = 139 c. m 1 = 141, m 2 = 84, m 3 = 139 b. m 1 = 135, m 2 = 84, m 3 = 96 d. m 1 = 141, m 2 = 45, m 3 = 141 Name the congruent angles and sides for the pair of congruent triangles ΔSKL ΔFG a. S G, K F, L, SK GF, KL F, SL G b. S F, K G, L, SK FG, KL G, SL F c. S, K F, L G, SK F, KL FG, SL G d. S G, K, L F, SK G, KL F, SL GF 105. ΔMG ΔWYT a. M T, G Y, W, MG TY, G YW, M TW b. M T, G W, Y, MG TW, G WY, M TY c. M W, G Y, T, MG WY, G YT, M WT d. M Y, G T, W, MG YT, G TW, M YW 27

28 Name: I: Identify the congruent triangles in the figure a. ΔKLJ ΔONM c. ΔLJK ΔOMN b. ΔKJL ΔOMN d. ΔJKL ΔONM 107. a. ΔSRT ΔWUV c. ΔSTR ΔWVU b. ΔRST ΔWVU d. ΔTRS ΔWUV etermine whether ΔPQR ΔSTU given the coordinates of the vertices. Explain PÊ Ë Á 0, 3 ˆ, Q Ê Ë Á0, 1 ˆ, R Ê Ë Á 2, 1 ˆ, S Ê Ë Á1, 2 ˆ, T Ê Ë Á1, 2 ˆ, U Ê ËÁ 1, 2 ˆ a. No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU. b. Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU. c. No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU. d. Yes; oth triangles have an obtuse angle PÊ Ë Á 3, 2 ˆ, Q Ê Ë Á1, 2 ˆ, R Ê Ë Á 1, 4 ˆ, S Ê Ë Á 4, 3 ˆ, T Ê Ë Á 2, 1 ˆ, U Ê ËÁ 0, 3 ˆ a. Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU. b. No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU. c. No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU. d. Yes; oth triangles have three sides. 28

29 Name: I: 110. PÊ Ë Á 2, 3 ˆ, Q Ê Ë Á 4, 2 ˆ, R Ê Ë Á 1, 4 ˆ, S Ê Ë Á2, 3 ˆ, T Ê Ë Á1, 2 ˆ, U Ê ËÁ 1, 3 ˆ a. Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU. b. No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU. c. No; Neither side has a right angle. d. Yes; Two sides of triangle PQR and angle PQR are the same measure as the corresponding sides and angle of triangle STU PÊ Ë Á 3, 2 ˆ, Q Ê Ë Á 2, 3 ˆ, R Ê Ë Á 1, 4 ˆ, S Ê Ë Á2, 4 ˆ, T Ê Ë Á3, 1 ˆ, U Ê ËÁ 4, 6 ˆ a. Yes; oth triangles have three acute angles. b. No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU. c. No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU. d. Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU PÊ Ë Á 4, 0 ˆ, Q Ê Ë Á2, 3 ˆ, R Ê Ë Á 1, 4 ˆ, S Ê Ë Á 1, 4 ˆ, T Ê Ë Á1, 1 ˆ, U Ê ËÁ 4, 6 ˆ a. Yes; Two sides of triangle PQR and angle PQR are the same measure as the corresponding sides and angle of triangle STU. b. Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU. c. No; One of the triangles is obtuse. d. No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU. Refer to the figure. ΔRM, ΔMX, and ΔXFM are all isosceles triangles If m FX = 96, what is m FMR? a. 96 c. 152 b. 134 d If m FMR = 155, what is m FMX? a. 45 c. 65 b. 55 d

30 Name: I: 115. Triangle FJH is an equilateral triangle. Find x and y. a. x = 7 5, y = 16 c. x = 7 5, y = 14 b. x = 7, y = 16 d. x = 7, y = Triangle RSU is an equilateral triangle. RT bisects US. Find x and y. a. x = 3, y = 18 c. x = 3, y = 42 b. x = 12, y = 42 d. x = 12, y = 18 Identify the type of congruence transformation a. reflection c. rotation b. translation d. not a congruence transformation 30

31 Name: I: 118. a. reflection or translation c. rotation or translation b. translation only d. rotation only Position and label the triangle on the coordinate plane right isosceles Δ with congruent sides and a units long a. c. b. d. 31

32 Name: I: 120. right ΔHJK with non-hypotenuse side HJ twice as long as non-hypotenuse side HK a units a. c. b. d isosceles ΔLMN with base LN 2b units long a. c. b. d. 32

33 Name: I: 122. equilateral ΔLMN with height a units and one-half base LN b units a. c. b. d right Δ with hypotenuse, leg 4a units long, and leg one-fourth the other leg a. c. b. d. 33

34 Name: I: 124. one-half equilateral triangle with SU bisecting the triangle at height a units and base ST 2b units a. c. b. d right ΔLMN with hypotenuse MN 5a units and base LM 3a units a. c. b. d. 34

35 Name: I: 126. equilateral ΔZYX with height c units and base XY 2d units a. c. b. d isosceles Δ with half the length of the base and bisecting the base a. c. b. d. 35

36 Name: I: 128. isosceles ΔFGH with GI twice the length of the base and bisecting the base a. c. b. d. etermine the relationship between the measures of the given angles PT, VPT a. PT > VPT c. PT = VPT b. PT < VPT etermine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain , 9, 10 a. Yes; the third side is the longest. b. No; the sum of the lengths of two sides is not greater than the third. c. No; the first side is not long enough. d. Yes; the sum of the lengths of any two sides is greater than the third , 14.5, 17.1 a. Yes; the third side is the longest. b. No; the first side is not long enough. c. Yes; the sum of the lengths of any two sides is greater than the third. d. No; the sum of the lengths of two sides is not greater than the third. 36

37 Name: I: 132. Find the measure of an interior angle of a regular polygon with 14 sides. Round to the nearest tenth if necessary. a c b d Find the measure of each exterior angle for a regular nonagon. Round to the nearest tenth if necessary. a c. 360 b. 140 d. 40 omplete the statement about parallelogram a. G; Opposite sides of parallelograms are congruent. b. ; iagonals of parallelograms bisect each other. c. ; Opposite sides of parallelograms are congruent. d. G; iagonals of parallelograms bisect each other. Refer to parallelogram to answer to following questions re the diagonals congruent? Justify your answer. a. Yes; oth diagonals have a length of b. Yes; oth diagonals have a length of 6 2. c. Yes; oth diagonals have a length of 3 2. d. No; The lengths of the diagonals are not the same. 37

38 Name: I: Refer to parallelogram to answer the following questions re the diagonals congruent? Justify your answer. a. Yes; oth diagonals have a length of 73. b. Yes; oth diagonals have a length of 13. c. Yes; oth diagonals have a length of d. No; The lengths of the diagonals are not the same. etermine whether a figure with the given vertices is a parallelogram. Use the method indicated (3, 9), (10, 1), (4, 10), ( 9, 3); istance and Slope Formulas a. No; The opposite sides are not congruent and do not have the same slope. b. Yes; The opposite sides do not have the same slope. c. No; The opposite sides do not have the same slope. d. Yes; The opposite sides are not congruent and do not have the same slope. Given each set of vertices, determine whether parallelogram is a rhombus, a rectangle, or a square. List all that apply (5, 10), (4, 10), (4, 9), (5, 9) a. square; rectangle; rhombus c. square b. rhombus d. rectangle 139. For trapezoid JKLM, and are midpoints of the legs. Find ML. a. 65 c. 28 b d. 3 38

39 Name: I: 140. For trapezoid JKLM, and are midpoints of the legs. Find. a. 23 c. 35 b. 8 d. 46 Position and label each quadrilateral on the coordinate plane rectangle with side length b units and height d units a. c. b. d. 39

40 Name: I: 142. square with side length b units a. c. b. d trapezoid with height d units, bases b and b + k units a. c. b. d. 40

41 Name: I: 144. parallelogram with side length d units and height b units a. c. b. d rectangle with side length 2k units and height 4k a. c. b. d. 41

42 Name: I: 146. square with side length 4k units a. c. b. d rectangle with side length 4k units and height 2k units a. c. b. d. 42

43 Name: I: 148. square with side length 2k units a. c. b. d isosceles trapezoid with height c units, bases 4d units and 2d units a. c. b. d. 43

44 Name: I: 150. isosceles trapezoid with height c units, bases 8d units and 4d units a. c. b. d. 44

45 I: GEM 8 MI-TERM REVIEW FOR WINTER REK nswer Section MULTIPLE HOIE 1. NS: PTS: 1 IF: asic REF: Lesson 0-1 OJ: onvert units of measure within the customary and metric systems. TOP: hanging units of measure within systems. KEY: Units of Measure Within Systems 2. NS: PTS: 1 IF: asic REF: Lesson 0-1 OJ: onvert units of measure within the customary and metric systems. TOP: hanging units of measure within systems. KEY: Units of Measure Within Systems 3. NS: PTS: 1 IF: asic REF: Lesson 0-2 OJ: onvert units of measurement between the customary and metric systems. TOP: hanging units of measure between systems. KEY: Units of Measure etween Systems 4. NS: PTS: 1 IF: asic REF: Lesson 0-2 OJ: onvert units of measurement between the customary and metric systems. TOP: hanging units of measure between systems. KEY: Units of Measure etween Systems 5. NS: PTS: 1 IF: asic REF: Lesson 0-3 OJ: Find the probability of simple events. TOP: Simple probability. KEY: probability 6. NS: PTS: 1 IF: asic REF: Lesson 0-3 OJ: Find the probability of simple events. TOP: Simple probability. KEY: probability 7. NS: PTS: 1 IF: asic REF: Lesson 0-4 OJ: Use the order of operations to evaluate algebraic expressions. TOP: lgebraic expressions. KEY: lgebraic expressions 8. NS: PTS: 1 IF: asic REF: Lesson 0-4 OJ: Use the order of operations to evaluate algebraic expressions. TOP: lgebraic expressions. KEY: lgebraic expressions 9. NS: PTS: 1 IF: asic REF: Lesson 0-5 OJ: Use algebra to solve linear equations. TOP: Linear equations. KEY: Linear Equations 10. NS: PTS: 1 IF: asic REF: Lesson 0-5 OJ: Use algebra to solve linear equations. TOP: Linear equations. KEY: Linear Equations 11. NS: PTS: 1 IF: asic REF: Lesson 0-6 OJ: Use algebra to solve linear inequalities. TOP: Linear inequalities. KEY: Linear Inequalities 12. NS: PTS: 1 IF: asic REF: Lesson 0-6 OJ: Use algebra to solve linear inequalities. TOP: Linear inequalities. KEY: Linear Inequalities 13. NS: PTS: 1 IF: asic REF: Lesson 0-7 OJ: Name and graph points in the coordinate plane. TOP: Ordered pairs. KEY: ordered pair x-coordinate y-coordinate quadrant origin 1

46 I: 14. NS: PTS: 1 IF: asic REF: Lesson 0-7 OJ: Name and graph points in the coordinate plane. TOP: Ordered pairs. KEY: ordered pair x-coordinate y-coordinate quadrant origin 15. NS: PTS: 1 IF: asic REF: Lesson 0-8 OJ: Use graphing, substitution, and elimination to solve systems of linear equations. TOP: Systems of linear equations. KEY: system of equations substitution elimination 16. NS: PTS: 1 IF: asic REF: Lesson 0-8 OJ: Use graphing, substitution, and elimination to solve systems of linear equations. TOP: Systems of linear equations. KEY: system of equations substitution elimination 17. NS: PTS: 1 IF: asic REF: Lesson 0-9 OJ: Evaluate square roots and simplify radical expressions. TOP: Square roots and simplifying radicals. KEY: Product Property Quotient Property 18. NS: PTS: 1 IF: asic REF: Lesson 0-9 OJ: Evaluate square roots and simplify radical expressions. TOP: Square roots and simplifying radicals. KEY: Product Property Quotient Property 19. NS: Line n contains points,, and. Line p contains points G and F. Only line contains point J. Is point J on that line? What points are on that line? What points are on that line? PTS: 1 IF: asic REF: Lesson 1-1 OJ: Identify and model points, lines, and planes. ST: L M.912.G.8.1 TOP: Identify and model points, lines, and planes. KEY: Points Lines Planes 20. NS: plane is a flat surface made up of points. plane is named by a capital script letter or by the letters naming three noncollinear points. Is that the way you name a plane? Is that the way you name a plane? o three collinear points name a plane? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify and model points, lines, and planes. TOP: Identify and model points, lines, and planes. ST: L M.912.G.8.1 KEY: Points Lines Planes 2

47 I: 21. NS: line is made up of points with an arrowhead at each end.,, and are points on line n. line is represented by line or but not just. re those points on line n? re those points on line n? Is that how a line is named? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify and model points, lines, and planes. ST: L M.912.G.8.1 TOP: Identify and model points, lines, and planes. KEY: Points Lines Planes 22. NS: line is made up of points and has no thickness or width. It is drawn with an arrowhead at each end. J,, and are points on line m. line is represented by line J or J but not just J. re those points on line m? Is that how you name a line? Is that how you name a line? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify and model points, lines, and planes. ST: L M.912.G.8.1 TOP: Identify and model points, lines, and planes. KEY: Points Lines Planes 23. NS: Line m contains points J,, and. Line p contains points G and F. Only line contains point. Is point on that line? Is that a line? What points are on that line? PTS: 1 IF: asic REF: Lesson 1-1 OJ: Identify and model points, lines, and planes. TOP: Identify and model points, lines, and planes. ST: L M.912.G.8.1 KEY: Points Lines Planes 3

48 I: 24. NS: The points not contained in or FG are J,, and H. K is the plane. Is that a point or the plane? Is that point on one of the lines listed? Is that point on one of the lines listed? PTS: 1 IF: asic REF: Lesson 1-1 OJ: Identify and model points, lines, and planes. ST: L M.912.G.8.1 TOP: Identify and model points, lines, and planes. KEY: Points Lines Planes 25. NS: The proper way to refer to a line is any 2 points on the line with an arrow above them or line such-and-such, where such-and-such is any 2 points on the line. Using three letters is not correct. oes line contain point J? oes that line contain points and? re points J and on line? PTS: 1 IF: asic REF: Lesson 1-1 OJ: Identify and model points, lines, and planes. TOP: Identify and model points, lines, and planes. 26. NS: ollinear points are points on the same line. ST: L M.912.G.8.1 KEY: Points Lines Planes re those points on the same line? What does collinear mean? re those points on the same line? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify collinear points. ST: L M.912.G.8.1 TOP: Identify collinear points. KEY: ollinear Points 4

49 I: 27. NS: ollinear points are points on the same line. re those points on the same line? re those points on the same line? What does collinear mean? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify collinear points. ST: L M.912.G.8.1 TOP: Identify collinear points. KEY: ollinear Points 28. NS: Points that lie on the same plane are said to be coplanar. Lines are made up of points. If line c intersects only with line b, then lines a and c must be parallel. oes line c intersect line a? What does coplanar mean? re lines a and c parallel? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify coplanar points. ST: L M.912.G.8.1 TOP: Identify coplanar points. KEY: oplanar Points Intersecting Lines Lines in Space 29. NS: Points that lie on the same plane are said to be coplanar. Three points are always coplanar but if the fourth point is not on the same plane with the first three, they are not all coplanar. o all four points lie on the same plane? Which plane? o all four points lie on the same plane? Which plane? What does coplanar mean? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify coplanar points. ST: L M.912.G.8.1 TOP: Identify coplanar points. KEY: oplanar Points Intersecting Lines Lines in Space 5

50 I: 30. NS: ollinear points are points on the same line. You are looking for collinear points, not coplanar points. re those points on the same line? What is meant by collinear? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify intersecting lines and planes in space. TOP: Identify intersecting lines and planes in space. 31. NS: ollinear points are points on the same line. ST: L M.912.G.8.1 KEY: Planes Planes in Space What plane are you working with? Which points should be collinear? What does collinear mean? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify intersecting lines and planes in space. TOP: Identify intersecting lines and planes in space. 32. NS: oplanar points are points that lie on the same plane. ST: L M.912.G.8.1 KEY: Planes Planes in Space Is K in a different plane? What plane are you working with? What plane are you working with? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify intersecting lines and planes in space. TOP: Identify intersecting lines and planes in space. ST: L M.912.G.8.1 KEY: Planes Planes in Space 6

51 I: 33. NS: oplanar points are points that lie on the same plane. What is the definition of coplanar? re all the points in the same plane? What is the definition of coplanar? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify intersecting lines and planes in space. TOP: Identify intersecting lines and planes in space. 34. NS: The intersection of two planes is a line. ST: L M.912.G.8.1 KEY: Planes Planes in Space an the intersection of two planes be a point? Is point on plane GFL? an the intersection of two planes be a plane? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify intersecting lines and planes in space. ST: L M.912.G.8.1 TOP: Identify intersecting lines and planes in space. KEY: Planes Planes in Space 35. NS: In this diagram two planes contain point K the front end of the prism and the top face of the prism. Is there another one? Is point K on plane L? Is there another one? PTS: 1 IF: verage REF: Lesson 1-1 OJ: Identify intersecting lines and planes in space. TOP: Identify intersecting lines and planes in space. ST: L M.912.G.8.1 KEY: Planes Planes in Space 7

52 I: 36. NS: Solve for a first using the two values of LM. LN = LM + MN. Solve for LN. Which two segments in the question are the same? Which two segments in the question are the same? Which segment are you solving for? PTS: 1 IF: asic REF: Lesson 1-2 OJ: ompute with measures. ST: M.912.G.1.2 M.912.G.8.6 TOP: ompute with measures. KEY: Measurement ompute Measures 37. NS: Since GK 104 bisects FGH, x = y and 7w + 3 =. Solve for w. 2 You are given the measure of FGH, not KGH. You are not finding the measure of FGK. You are finding w. Why did you divide by 2? PTS: 1 IF: verage REF: Lesson 1-4 OJ: Identify and use congruent angles. TOP: Identify and use congruent angles. KEY: ngles ongruent ngles ongruency 38. NS: MKH > 90, so it is obtuse. ST: M.912.G.1.2 M.912.G.8.4 If answer d is true, then this must be true. eing in the interior means being between the two end rays of an angle. If answer b is true, then this must be true. PTS: 1 IF: asic REF: Lesson 1-4 OJ: Identify and use the bisector of an angle. TOP: Identify and use the bisector of an angle. ST: M.912.G.1.2 M.912.G.8.4 KEY: ngle isectors 8

53 I: 39. NS: m JKN = 2 ( m 1) = 90 What is the definition of "right angle"? What is the definition of "right angle"? You are solving for t. PTS: 1 IF: verage REF: Lesson 1-4 OJ: Identify and use the bisector of an angle. ST: M.912.G.1.2 M.912.G.8.4 TOP: Identify and use the bisector of an angle. KEY: ngle isectors 40. NS: Vertical angles are two nonadjacent angles formed by two intersecting lines. cute angles measure less than 90 degrees. You are looking for vertical angles, not adjacent angles. You are looking for vertical angles, not a linear pair. What is the definition of acute? PTS: 1 IF: asic REF: Lesson 1-5 OJ: Identify and use special pairs of angles. ST: M.912.G.1.2 M.912.G.8.2 TOP: Identify and use special pairs of angles. KEY: djacent ngles Vertical ngles Linear Pair omplementary ngles Supplementary ngles 41. NS: djacent angles are two angles that lie in the same plane, have a common vertex, and a common side, but no common interior points. Obtuse angles measure greater than 90 degrees. You are looking for adjacent angles, not vertical angles. You are looking for adjacent angles, not a linear pair. What is the definition of obtuse? PTS: 1 IF: asic REF: Lesson 1-5 OJ: Identify and use special pairs of angles. ST: M.912.G.1.2 M.912.G.8.2 TOP: Identify and use special pairs of angles. KEY: djacent ngles Vertical ngles Linear Pair omplementary ngles Supplementary ngles 9

54 I: 42. NS: linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. You are looking for a linear pair, not vertical angles. You are looking for a linear pair, not just adjacent angles. You are looking for a linear pair which, by definition, must be adjacent. PTS: 1 IF: verage REF: Lesson 1-5 OJ: Identify and use special pairs of angles. ST: M.912.G.1.2 M.912.G.8.2 TOP: Identify and use special pairs of angles. KEY: djacent ngles Vertical ngles Linear Pair omplementary ngles Supplementary ngles 43. NS: Supplementary angles are two angles whose measures have a sum of 180. What is the definition of supplementary? o the measures have a sum of 180 degrees? What is the definition of supplementary? PTS: 1 IF: asic REF: Lesson 1-5 OJ: Identify and use special pairs of angles. ST: M.912.G.1.2 M.912.G.8.2 TOP: Identify and use special pairs of angles. KEY: djacent ngles Vertical ngles Linear Pair omplementary ngles Supplementary ngles 44. NS: Vertical angles are two nonadjacent angles formed by two intersecting lines. Obtuse angles measure greater than 90 degrees. You are looking for vertical angles, not adjacent angles. What is the definition of obtuse? You are looking for vertical angles, not a linear pair. PTS: 1 IF: asic REF: Lesson 1-5 OJ: Identify and use special pairs of angles. ST: M.912.G.1.2 M.912.G.8.2 TOP: Identify and use special pairs of angles. KEY: djacent ngles Vertical ngles Linear Pair omplementary ngles Supplementary ngles 10

55 I: 45. NS: Supplementary angles are two angles whose measures have a sum of 180. What is the definition of supplementary? What is the sum of those two measures? Is the measure of one angle 26 more than the other? PTS: 1 IF: verage REF: Lesson 1-5 OJ: Identify and use special pairs of angles. ST: M.912.G.1.2 M.912.G.8.2 TOP: Identify and use special pairs of angles. KEY: djacent ngles Vertical ngles Linear Pair omplementary ngles Supplementary ngles 46. NS: Suppose the line containing each side is drawn. If any of the lines contain any point in the interior of the polygon, then it is concave. Otherwise it is convex. convex polygon in which all the sides are congruent and all the angles are congruent is called a regular polygon. If it is regular the angles and sides would all be congruent. If it is concave, lines drawn from the segments would pass through the polygon. ount the number of sides. PTS: 1 IF: asic REF: Lesson 1-6 OJ: Name polygons. ST: M.912.G.2.5 M.912.G.2.6 M.912.G.2.1 M.912.G.2.7 TOP: Name polygons. KEY: Polygons Name Polygons 47. NS: Suppose the line containing each side is drawn. If any of the lines contain any point in the interior of the polygon, then it is concave. Otherwise it is convex. convex polygon in which all the sides are congruent and all the angles are congruent is called a regular polygon. If it is regular, the angles and sides would all be congruent. If it is concave, lines drawn from the segments would pass through the polygon. ount the number of sides. PTS: 1 IF: verage REF: Lesson 1-6 OJ: Name polygons. ST: M.912.G.2.5 M.912.G.2.6 M.912.G.2.1 M.912.G.2.7 TOP: Name polygons. KEY: Polygons Name Polygons 11

56 I: 48. NS: Perimeter is the sum of the sides. id you find the value of r? What is the value of r? What is the sum of the sides? PTS: 1 IF: verage REF: Lesson 1-6 OJ: Find perimeter of two-dimensional figures. ST: M.912.G.2.5 M.912.G.2.6 M.912.G.2.1 M.912.G.2.7 TOP: Find the perimeters of polygons. KEY: Perimeter Polygons 49. NS: The area of a rectangle is the product of its length and width. = l w You need to multiply not add. Place the decimal in the correct position. You have calculated the perimeter. PTS: 1 IF: asic REF: Lesson 1-6 OJ: Find area of two-dimensional figures. ST: M.912.G.2.5 M.912.G.2.6 M.912.G.2.1 M.912.G.2.7 TOP: Find area of two-dimensional figures. KEY: rea Two-imensional Figures 50. NS: This solid is a cylinder. The bases of a cylinder are circles. In this cylinder, the circular bases are centered at points and, thus the correct answer is ñ and ñ. The bases of a cylinder are circles, not segments. The bases of a cylinder are circles, not segments. Those are the wrong centers for the circular bases. PTS: 1 IF: asic REF: Lesson 1-7 OJ: Identify three-dimensional figures. TOP: Identify three-dimensional figures. ST: M.912.G.7.1 M.912.G.7.2 KEY: Three-imensional Figures 12

57 I: 51. NS: The bases of a prism are congruent, parallel polygons. Here those polygons are the right triangles UWY and VXZ. re those polygons congruent and parallel? The bases of a prism are congruent, parallel polygons. re those polygons parallel? PTS: 1 IF: asic REF: Lesson 1-7 OJ: Identify three-dimensional figures. ST: M.912.G.7.1 M.912.G.7.2 TOP: Identify three-dimensional figures. KEY: Three-imensional Figures 52. NS: In a solid, all points that represent intersections of edges are vertices. Therefore all of the points shown are vertices. That s only half right. That s only half right. There are more vertices than that. PTS: 1 IF: asic REF: Lesson 1-7 OJ: Identify three-dimensional figures. ST: M.912.G.7.1 M.912.G.7.2 TOP: Identify three-dimensional figures. KEY: Three-imensional Figures 53. NS: Start with 1. dd, subtract, or multiply the same number to each number to get the next one. What operations are involved? idn t you carry the conjecture too far? heck your math. PTS: 1 IF: asic REF: Lesson 2-1 OJ: Make conjectures based on inductive reasoning. TOP: Make conjectures based on inductive reasoning. ST: L M.912.G.8.3 KEY: Inductive Reasoning onjectures 13

58 I: 54. NS: oplanar points always lie in the same plane. Three points are always coplanar but four are not. What does coplanar mean? What does coplanar mean? re more than two points always coplanar? PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 55. NS: oncave polygons must be irregular. This means all sides and angles are not congruent. What is the definition of concave? Is that counterexample correct? What is the definition of concave? PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 56. NS: ngles are congruent only if their measures are equal. Point may be closer to line or line so the measures would not be equal. What is the definition of congruent? What is the definition of congruent? Would that be a counterexample? PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 14

59 I: 57. NS: ecause m is squared in the example, m could be positive or negative. Subtract 6 from both sides. What about negative numbers? Subtract 6 from both sides. PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 58. NS: oplanar points always lie in the same plane. Three points are always coplanar but four are not. What does coplanar mean? What does coplanar mean? Would the points have to be in the same plane? PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 59. NS: Just because two angles share a common point does not mean they are vertical. They could be nearly adjacent or one could be in the interior of the other one. What is a vertical angle? What is a vertical angle? What is a vertical angle? PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 15

60 I: 60. NS: If two angles are supplementary their measures total 180. Either both are right or one is obtuse and the other acute. What is the definition of supplementary? What is the definition of supplementary? What is the definition of supplementary? PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 61. NS: If two angles are supplementary their measures total 180. F could only be supplementary to H if they are both right angles. What is the definition of supplementary? What is the definition of supplementary? What is the definition of supplementary? PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 62. NS: Unless there are specific angle measures mentioned, even though the angles in the picture may look congruent you cannot assume that they are congruent. What is the definition of congruent? What is the definition of congruent? What is the definition of congruent? PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 16

61 I: 63. NS: Even though they have a common point, the two segments do not have to be on the same line. What is the definition of midpoint? What is the definition of midpoint? What is the definition of midpoint? PTS: 1 IF: asic REF: Lesson 2-1 OJ: Find counterexamples. ST: L M.912.G.8.3 TOP: Find counterexamples. KEY: ounterexamples 64. NS: Two or more statements can be joined to form a compound statement. conjunction is a compound statement formed by joining two or more statements with the word and. disjunction is a compound statement formed by joining two or more statements with the word or. The symbol for logical and is. The symbol for logical or is. How many sides does a decagon have? What is the symbol for logical and? What is the symbol for logical and? PTS: 1 IF: verage REF: Lesson 2-2 OJ: etermine truth values of conjunctions and disjunctions. ST: M TOP: etermine truth values of conjunctions and disjunctions. KEY: Truth Values onjunctions isjunctions 65. NS: The first statement column in a truth table contains half Ts, half Fs, grouped together. The second statement column in a truth table contains the same, but they are grouped by half the number that the first column was. The third statement column contains the same but they are grouped by half the number that the second column was. Use the truth values of the first three columns to determine the truth values for the last two columns. The symbol for not is. The symbol for logical and is. heck the values for the last two columns carefully. o your statement columns show every possible T and F combination? heck the values for the last two columns carefully. PTS: 1 IF: verage REF: Lesson 2-2 OJ: onstruct truth tables. ST: M TOP: onstruct truth tables. KEY: Truth Tables 17