Practice. 8. Use inductive reasoning to determine the next two terms in the sequence. a. 1, 3, 7, 15, 31, b. 3, -6, 12, -24, 48,
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1 CTIC CTIVITY Which is the correct name for this line? G M a. G c. MG b. GM d. M 2. Use the diagram to name each of the following. L M a. parallel lines b. perpendicular lines. In this diagram, m SUT = 25. U a. Name another angle that has measure 25. b. Name a pair of complementary angles. c. Name a pair of supplementary angles. T N S Use this circle for Items 7. T U W. Name the radii of circle. 5. Name the diameter(s) in circle. 6. Name the chord(s) in circle. 7. Which statement below must be true about circle? a. The distance from U to W is the same as the distance from to T. b. The distance from U to W is the same as the distance from to J. c. The distance from to T is half the distance from to. d. The distance from to T is twice the distance from to J. CTIVITY Use inductive reasoning to determine the next two terms in the sequence. a. 1,, 7, 15, 1, b., -6, 12, -2, 8, 9. Write the first five terms of two different sequences for which 2 is the third term. 10. Generate a sequence using the description: the first term in the sequence is 2 and the terms increased by consecutive odd numbers beginning with. J ctivity a. LN b. LN M or M a. U b. U and U or SUT and U c. U and US, SUT and US, TU and TUS, U and UT, U and UT, U and US., J, T 5. T 6. UW, T 7. ctivity 1.2 8a. 6, 127 b. -96, nswers may vary. Sample answer: 6, 12, 2, 8, 96, and 1, 19, 2, 29,, 10. 2, 5, 10, 17, 26, Unit 1 roof, arallel and erpendicular Lines 8 Unit 1 roof, arallel and erpendicular Lines 8
2 CTIC Continued 11a. ractice 11. Use this picture pattern. CTIVITY 1. b. 2, 6, 12, 20, 0 c. nswers may vary. Sample answer: the first term is 2 then add consecutive even numbers starting with. 12. (2m + 1) * (2p + 1) = mp + 2m + 2p + 1 = 2(2mp + m + p) + 1 which is odd because it is in the form 2 times an integer plus 1. ctivity See below. 15. nswers may vary. Sample answer: If two numbers are even, then their sum is even. 16. tomorrow is Friday 17. If tomorrow is Friday, then today is Thursday. 18. If today is not Thursday, then tomorrow is not Friday. 19. If tomorrow is not Friday, then today is not Thursday. 20. nswers may vary. Sample answer: a balloon. 21. nswers may vary. Sample answer: If x =, then x + 1 = 5. a. raw the next shape in the pattern, b. Write a sequence of numbers that could be used to express the pattern, c. Verbally describe the pattern of the sequence. 12. Use expressions for odd integers to confirm the conjecture that the product of two odd integers is an odd integer. CTIVITY Identify the property that justifies the statement: 5(x ) = 5x 15 a. multiplication b. transitive c. subtraction d. distributive 1. Complete the prove statement and write a two column proof for the equation: Given: 5(x 2) = 2x rove: 15. Write the statement in if-then form. The sum of two even numbers is even. Use this statement for Items If today is Thursday, then tomorrow is Friday. 16. State the conclusion of the statement. 17. Write the converse of the statement. 18. Write the inverse of the statement. 19. Write the contrapositive of the statement. 20. Given the false conditional statement, If a vehicle is built to fly, then it is an airplane, write a counter example. 21. Give an example of a statement that is false and logically equivalent to its inverse. Construct a truth table for each of the following compound statements. 22. p q 2. p q 2. ( p q) 25. p (q p) CTIVITY If is between and M and M = 7. and M = 8.5, then = a. 5.8 b. 1.2 c. 7. d Given: K is between H and J, HK = 2x - 5, KJ = x +, and HJ = 2. What is the value of x? a. 9 b. 5 c. 19 d. 28. If K is the midpoint of HJ, HK = x + 6, and HJ = x - 6, then KJ =?. a. 15 b. 9 c. d lies in the interior of ST. m S = 0 and m TS = 10. m ST =? a. 100 b. 50 c. 0 d S bisects. If m S = x and m S = 2x + 6, then m =?. a. 18 b. 6 c. 0 d and are supplementary. m = 5x + and m = x +. x =? a. 1 b. 0 c. 29 d. 0 ctivity Step 1 Step 2 Step p q ~q p ~q T T F F F T F T F F T T 2. Step 1 Step 2 Step p q ~q p ~q T T F F F T F F F F T F 8 SpringBoard Mathematics with Meaning Geometry 1. Given: 5(x - 2) = 2x - rove: x = 2 Statements easons 1. 5(x - 2) = 2x - 1. Given 2. 5x - 10 = 2x - 2. istributive roperty. x - 10 = -. Subtraction roperty of quality. x = 6. ddition roperty of quality 5. x = 2 5. ivision roperty of quality 8 SpringBoard Mathematics with Meaning Geometry
3 CTIC Continued In this figure, CG, m BHC = 20, and m H = 60. Use this figure determine the angle measures for Items In this figure, m 1 = x + 50 and m = 2x Show all work for parts a, b, and c. 2. See below. 25. G F H C B 1 2 Step 1 Step 2 Step p q q p p (q p) T T T T F T F F F F T T ctivity m CH. m HF. m GHF 5. m H 6. In this figure, m = x + 18, m = x + 15, and m 5 = x +. Show all work for parts a, b, and c. b. What is the measure of m? c. What is the measure of m 2? 8. Given: B, bisects C, m CB = 2x - and m C = x + 1. Show all work for parts a and b. 26. B 27. B B 0. B 1 5 b. What is the measure of 1 c. Is complementary to 1? xplain. b. What is the measure of m C? C B 1. C a. x = 2 b. m 1 = 2 c. No; Since and 1 are vertical angles, they are equal; + 1 = 8 7a. x = 8 b. m = 82 c. m 2 = 98 8a. x = 16 b. m C = 1 Unit 1 roof, arallel and erpendicular Lines Step 1 Step 2 Step Step p q ~p ~p q ~(~p q) T T F T F T F F F T F T T T F F F T T F Unit 1 roof, arallel and erpendicular Lines 85
4 CTIC Continued ctivity and and and x = 1, m = 80 CTIVITY 1.6 ractice Use this diagram for Items n l 9. If l n and m n, then m =? 50. If l n and m l, then m 1 =?. CTIVITY 1.7 Use this diagram to identify the property, postulate, or theorem that justifies each statement in Items x = 15, m 10 = x = 20, m 8 = 118 8a. m 16 =15 because vertical angles are b. m 15 = 5 Sample justification: Vertical angles are congruent ( 10 16). Then, if lines are parallel, the sameside interior angles are supplementary. c. m 8 = 15 Sample justification: if lines are parallel, then corresponding angles are d. m 1 = 75 Sample justification: if lines are parallel, then corresponding angles are e. m = 105 Sample justification: Vertical angles are congruent ( 12 2). Then, if lines are parallel, the sameside interior angles are supplementary t List all angles in the diagram that form a corresponding angle pair with List all angles in the diagram that form an alternate interior angle pair with List all angles in the diagram that form a same side interior angle pair with Given l n. If m 6 = 120, then m 16 =?.. Given l n. If m 12 = 5x +10 and m 1 = 6x -, then x =? and m =?.. Given l n. If m 1 = 75, then m 2 =?. 5. Given l n. If m 9 = x + 12 and m 15 = 2x + 27, then x =? and m 10 =?. 6. Given l n. If m = 100, then m 2 =?. 7. Given l n. If m 16 = 5x + 18 and m 15 = x+ 2, then x =? and m 8 =?. 8. If m 10 = 15, m 12 = 75, and l n determine the measure of each angle. Justify each answer. a. m 16 b. m 15 c. m 8 d. m 1 e. m 86 SpringBoard Mathematics with Meaning Geometry m = a. ngle addition postulate b. ddition property c. efinition of congruent segments d. Segment addition postulate 52. If is the midpoint of, then. a. efinition of midpoint b. efinition of congruent segments c. efinition of segment bisector d. Segment addition postulate 5. a. efinition of linear pair b. efinition of congruent angles c. Vertical angles are d. efinition of angle bisector 5. If 1 is complementary to 2, then m 1 + m 2 = 90 a. ngle ddition ostulate b. ddition property c. efinition of perpendicular d. efinition of complementary 86 SpringBoard Mathematics with Meaning Geometry
5 CTIC Continued 55. If m = 90, then is a right angle. a. efinition of perpendicular b. efinition of complementary angles c. efinition of right angle d. Vertical angles are 56. Write a two-column proof. Given: a b, c d rove: 5 12 b CTIVITY Calculate the distance between the points (-, 2) and B(15, 6). 62. Calculate the distance between the points (1.5, 7) and S(-2., -8). 6. Kevin and Clarice both live on a street that runs through the center of town. If the police station marks the midpoint between their houses, at what point is the police station on the number line? ctivity C C 56. See below. a c CTIVITY 1.8 d etermine the slope of the line that contains the points with coordinates (1, 5) and (-2, 7). 58. Which of the following is NOT an equation for a line parallel to y = 1 2 x - 6? a. y = 2 x + 6 b. y = 0.5x - c. y = 2 1 x + 1 d. y = 2x etermine the slope of a line perpendicular to the line with equation 6x - y = Line m contains the points with coordinates (-, 1) and (5, 8), and line n contains the points with coordinates (6, -2) and (10, 7). re the lines parallel, perpendicular, or neither? Justify your answer Kevin s House Clarice s House 6. etermine the coordinates of the midpoint of the segment with endpoints (, 16) and S(7, -6). 65. etermine the coordinates of the midpoint of the segment with endpoints W(-5, 10.2) and X(12,.5). 66. Two explorers on an expedition to the rctic Circle have radioed their coordinates to base camp. xplorer is at coordinates (-26, -15). xplorer B is at coordinates (1, 21). The base camp is located at the origin. a. etermine the linear distance between the two explorers. b. etermine the midpoint between the two explorers. c. etermine the distance between the midpoint of the explorers and the base camp. ctivity Neither. nswers may vary. Sample justification: Two lines are parallel if they have the same slope and two lines are perpendicular if their slopes are negative reciprocals. The slope of line m is 7 9, and the slope of line n is 9. The slopes 7 9 and are neither 9 the same nor are they negative reciprocals. ctivity (5, 5) 65. (.5, 7.5) 66a. 2, b. (-6.5, ) 66c Unit 1 roof, arallel and erpendicular Lines nswers may vary. Sample proof: Given: a b, c d rove: 5 12 Statements easons 1. a b 1. Given If parallel lines are cut by a transversal, then corresponding angles are. c d. Given If parallel lines are cut by a transversal, then corresponding angles are Vertical angles are congruent Transitive property Unit 1 roof, arallel and erpendicular Lines 87
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