1. Sample answer: A, B, D. 3. D, E, F 4. plane C 6. C, E 7. E. 8. Sample answer: C ray infinite; zero. 4. no; yes 5.
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1 nswers hapter Start Thinking When the vertex of the triangle is moved in an direction, its angle measure also changes. ecause all three sides of the triangle are connected, this also affects the other angles; If one angle becomes lesser, the sum of the other angles must become greater, and vice versa. ll angles must be in relation to one another so that the sum of their angles alwas equals the same 1. amount ( ) 1.1 Warm Up 1. triangle. pentagon 3. hexagon. octagon 5. rhombus 6. decagon 1.1 Practice 1. Sample answer:,,., EF 3., E, F. plane 5. Sample answer: EG, EF 6., E 7. E. Sample answer: N 1.1 umulative Review Warm Up 1. b = 6. a = 6 3. c = 1. p = 5 5. c = 9 6. u = 11. a b 1.1 Practice 1. Sample answer:, E. Sample answer:, 3. plane G. line s 5. Sample answer: N, T, W 6. Sample answer:, N, V 7. V. c 1. plane; ecause three points determine a plane, the three feet of a tripod create a plane on the ground ra segment 15. infinite; zero c Sample answer: 1. H G X 1.1 Enrichment and Extension 1. Sample answer: plane PR, plane PQO, plane PON. PO 3. ST, SR, SN 11. Sample answer: L 1. EF Sample answer: 15. point, line. no; es 5. VW 6. plane TXW and plane VWX 7. plane ZVT, plane ZYT, plane ZVW. es; The onl place where all planes will meet in the pramid is at point T. opright ig Ideas Learning, LL ll rights reserved. Geometr nswers 1
2 nswers 9. es; When substituted into each equation, it is a solution. 1. no; It is not a solution to either equation. 1.1 Puzzle Time I LL EET YOU HLFWY IN THE ILE FOR SPLIT 1. Start Thinking Set the compass to be more than half the length of the line segment. raw a semicircle with the compass. Turn the compass around and do the same from the other side, so that the semicircles intersect above and below the line. Use the straightedge to connect the two intersections. The point where the new line intersects the original line is the midpoint of the original line. 1. Warm Up umulative Review Warm Up H F E G x The ruler is lined up at the -inch mark; = 5.5 = in. 11. true; F is on EG between E and G. 1. true; is on between and. 13. false;,, and F are not collinear. 1. Practice 1. 7 in.. 1 in. 3.. es es about 1 mi x 9. x + 5 = x + 3; x = 7; = 7; = 1; = x = 7; x = 6; = 53; = 1; = 7 x 1. Practice mi; the third da 1 in.. 5 in S. T V x T S x 1. Enrichment and Extension 1. a. 5 b. 5 c. 5 d. 7 e. 7 f. 95. a. b. 3 c. 9 d. 7 e. 9 f G or IL. 5. F U U V 6. x + x + 9x = 56; x = 7; L = 9; N = 175 no es 7. x + x + 1 = 13; x = 16; L = ; N = 9 5. V S T x U = + ; x = ; L = ; x 3 3 x LN = 3 es 1. Puzzle Time HE WS GOO RULER Geometr nswers opright ig Ideas Learning, LL ll rights reserved.
3 nswers 1.3 Start Thinking Plot the two points. raw a right triangle containing those points as vertices, along with a third point. Using the coordinate plane, calculate the side lengths of the legs 5 and 1. Then use the Pthagorean Theorem to find the length of the hpotenuse, = This is the distance in blocks between the points. 1.3 Warm Up umulative Review Warm Up 1. x = 6. x = 1 3. x = 69. x = Practice 1. line d; 3. L; R;. ; X 7. ( 3, ). (, ) 9. (, 7 ) 1. ( 7, 7) about about 5.7 cm; about. cm; The center of the square is the segment bisector of the diagonal ft 1.3 Practice 1. W; 3 3. E Not drawn to scale. line ; 3. (, 7 ) 5. (, 3 ) 6. ( 3, ) Y F 1. no; If one side of the square is s, then the length of the diagonal is s + s = s = s. 11. es; Sample answer: segment can be bisected b two different lines. 1. about mi; about 1.5 mi 1.3 Enrichment and Extension 1. 3x1 + x 31 + x1 + x 1 +,,,, x1 + 3x 1 + 3,. a. ( 3, 7 ), (, 5 ), ( 1, 13 ) b. (, 5 ), ( 1, 6 ), ( 7, 7) 3. 13; b 11. ( 1, 3 ) and (, 3) 5. es; The distance between each vertex is 5., 1, 6 7. ( 5, 6, 5 ). ( 7, 9, 3 ) 6. ( ) Puzzle Time IT WNTE TO E REUE 1. Start Thinking quad-, penta-, hexa-; Sample answer: quadraphonic sound is a form of surround sound involving four speakers. pentathlon is an athletic competition for individuals consisting of five events. hexapod is an animal having six feet, tpicall with three distinct sets of two legs. 1. Warm Up 1. P = 36 cm, = 6 cm. P = 7 in., = 36 in. 3. P = 5. in., = in.. P = cm, = cm 1. umulative Review Warm Up cm. 1 m 7. ( 5, 13 ). about opright ig Ideas Learning, LL ll rights reserved. Geometr nswers 3
4 nswers 1. Practice 1. quadrilateral; convex. hexagon; concave 3. about 16.5 units. 1 square units 5. square units 6. about.6 units 7. about 1.5 units. 3 square units 9. 1 square units 1. square units 11. ( 1, 3 ); 1 square units 1. a. 36 ft b. ft c. $1 1. Practice 1. heptagon; convex. decagon; concave 3. about. units. 7.5 square units 5. square units 6. about 13. units 7. about.6 units. 6 square units square units 1. square units 11. a. 1. mi 65 ft b. ft c. $.5 1. Enrichment and Extension 1. square units. x = or x = 3. a. about.63 square units b. about 3 squares c. about square units. about 1 square unit 1. Puzzle Time TOO NY PROLES 1.5 Start Thinking If the angle is larger than a right angle, it is obtuse. If the angle is smaller than a right angle, it is acute. 1.5 Warm Up 1. x = 7. r = n = Practice 1. XYZ, ZYX, Y. PQR, RQS, SQP ; obtuse. EH, FI 5. G, EH, HE, FI, IF x = a. Sample answer: EFG is acute, FE is right, F is obtuse, is straight. b. 31 angles c. 7 d Practice 1. 5 ; acute. 9 ; right ; obtuse. 1 ; straight es; ecause an acute angle is less than 9, the sum of three acute angles can be equal to a. Sample answer: E is acute, E is right, E is straight. b. E c. 5 d Enrichment and Extension 1. 6 < x < 51. m EG =, m FEG = 3. 6; x = 5, = = 9 5. t = w = umulative Review Warm Up 1. r =. w = 5 3. =. v = 5 E F Geometr nswers opright ig Ideas Learning, LL ll rights reserved.
5 nswers Puzzle Time IS RRIER 1.6 Start Thinking The angle formed is now greater than 1. So, add the angle formed from the negative x-axis to its position in Quadrant III to 1 to get the total angle measure. 1.6 Warm Up 1. x = 3. c = 1 3. x = 1. n = 5. x = x = 1.6 umulative Review Warm Up 1. n 1 =, n = 5 6 = 1, n = 3. ( n ) 1 = 7, n = 3. ( n ) x + 6 = x + x + + x + + 5, x = 1, x + = 3, x + = 5, x + 6 = 7. ( ) ( ) ( ) 1.6 Practice 1. FJG, GJH., EJF 3., EJG m WXY = 19, m YXZ = m =, m =. and 5 9. es; The sides form two pairs of opposite ras. 1. no; The sides do not form two pairs of opposite ras. + + = 1; 7 and x ( x ) 1. x + 3x = 9;.5 and = 1; 5 and x ( x ) 1. a. Sample answer: 1, b. Sample answer:, 5 c. 6 and 5, and 5 d. 6 ; 1 and 3 are vertical angles so the have the same angle measure. 1.6 Practice 1. E and E. E and HFJ 3. E and HFK m =, m = m WXY = 3, m YXZ = and, 3 and 9. 7 and 1. es; The sides form two pairs of opposite ras. 11. no; The sides do not form two pairs of opposite ras = 9; 7 and x ( x ) 13 x + x = 1; 36 and = 1; 6 and 9 1. x ( x ) 15. never; The sum of the angle measures of a linear pair is sometimes; When the sides of two angles form two pairs of opposite ras that meet at a 9 angle, the sum of the angle measures is Enrichment and Extension 1. supplementar. complementar 3. neither. supplementar 5. neither 6. complementar 7. complementar: not possible, supplementar: 1 5 π. complementar: not possible, supplementar: 19 π 9. complementar: 11 π, supplementar: π 1. complementar: 1 1 π, supplementar: 3 5 π opright ig Ideas Learning, LL ll rights reserved. Geometr nswers 5
6 nswers 11. complementar: 1 π, supplementar: 5 π 1. complementar: not possible, supplementar: 1 π perimeter = 7 km, area = km perimeter = 55. cm, area = cm 1.6 Puzzle Time EUSE THE TEHER SI IT WS PIEE OF KE umulative Review perimeter = 3. in., area = in in ft a 976 in. 16 ft b > c < d f > x = 11. x = 5 9. x = 3 5. x = x = x = x = x = x = x = 57. x = 5. x = x = 3 6. x = 61. x = 6 6. x = g 35. h 3. j < perimeter = cm, area = cm perimeter = mi, area = 16 mi. k < perimeter = in., area = 36 in perimeter = 6 d, area =.5 d 5. m < perimeter = 3 mm, area = 37.5 mm perimeter = 1 ft, area = 19.5 ft 6 Geometr nswers opright ig Ideas Learning, LL ll rights reserved.
7 nswers 6. n p 9 x s 1 9. t x 9. u > v > x = x = 3 9. x = 13 x 95. x = x = x = 6 9. x = 99. x = 1. x = x = 6 1. x = x = x = x = x = x = 1. x = x = x = x = x = x = 11. x = 115. x = ( ) 15. ( 3, 1), H ( 3, 7) 17. H ( 3, 1) or or or 3 13 x m = 5, m = 139. m LP =, m PN = 9 opright ig Ideas Learning, LL ll rights reserved. Geometr nswers 7
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