Answers for Lesson 3-1, pp Exercises
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1 Answers for Lesson -, pp. Eercises * ) PQ * ) PS * ) PS * ) PS * ) SR * ) QR * ) QR * ) QR. nd with trnsversl ; lt. int. '. nd with trnsversl ; lt. int. '. nd with trnsversl ; sme-side int. '. nd with trnsversl ; corr. ' 5. nd : corr. ' 6. nd : sme-side int. ' nd : lt. int. ' nd : corr. ' 5 nd 6: corr. ' 5 nd 6: corr. ' 7. nd : corr. ' 8. lt. int. ' nd : sme-side int. ' 5 nd 6: lt. int. ' 9.. Sme-Side Int. Angles Thm.. Sme-Side Int. Angles Thm. 5. Congruent Supplements Thm. 0.. (Given). (Alt. Int. ' Thm.). c d (Given). (Corr. ' Post.) 5. (Trns. Prop.) * ) SQ * ) SQ * ) PQ * ) SR. m 75 ecuse corr. ' of lines re ; m 05 ecuse sme-side int. ' of lines re suppl.. m 0 ecuse corr. ' of lines re ; m 60 ecuse sme-side int. ' of lines re suppl.. m 00 ecuse sme-side int. ' of lines re suppl.; m 70 ecuse lt. int. ' of lines hve mesure. Geometry Chpter 5
2 Answers for Lesson -, pp. Eercises (cont.). 70; 70, ; 65, ; 00, m m m 6 m 8 m 9 m m m 5 5; m m m 5 m 7 m 0 m m 8 8. You must find the mesure of one.all ' tht re vert., corr., or lt. int. to tht will hve tht mesure. All other ' will e the suppl. of tht mesure. 9. two 0. four. two. four.. 76, y 7, v, w , y 5 6. Trns mens cross or over. A trnsversl cuts cross other lines. 7. Answers my vry. Smple: E illustrtes corr. ' ( nd, nd ) nd sme-side int. ' ( nd, nd ); I illustrtes lt. int. ' ( nd, nd ) nd sme-side int. ' ( nd, nd ). 8.. (Given). re suppl. (Sme Side Int. ' Thm.). re suppl. (Sme Side Int. ' Thm.). (Given) 5. re suppl. (Sust.) 6. ( Suppl. Thm.) Geometry Chpter 5
3 Answers for Lesson -, pp. Eercises (cont.) 9. Since, ecuse they re corr. '. Also nd re supplementry y the Add. Post. So y Sust., nd re supplementry sme-side int. '.. lt. int. '. He knew tht lt. int. ' of lines re.. The ' leled re corr. ' nd should e. If you solve 60 60, you get 0. This would e impossile since 60 nd 60 would equl 0.. Never; the two plnes do not intersect.. Sometimes; if they re. 5. Sometimes; they my e skew. 6. Sometimes; they my e. Geometry Chpter 5
4 Answers for Lesson -, pp. 7 9 Eercises * BE ) * CG ). ; Conv. of Corr. ' Post.. CA HR; Conv. of Corr. ' Post.. JO LM; if two lines nd trnsversl form sme-side int. ' tht re suppl., then the lines re.. PQ ST; Conv. of Alt. Int. ' Thm The corr. ' re, so the lines re y the Conv. of Corr. ' Post. 0. ; if two lines nd trnsversl form sme-side int. ' tht re suppl., then the lines re.. ; if two lines nd trnsversl form sme-side int. ' tht re suppl., then the lines re.. ; if two lines nd trnsversl form sme side et. ' tht re suppl., then the two lines re.. none. ; Conv. of Corr. ' Post. 5. none 6. ; Conv. of Alt. Int. ' Thm. 7., m; Conv. of Corr. ' Post. 8. ; if two lines nd trnsversl form lt. et. ' tht re congruent, then the two lines re. 9. ; Conv. of Corr. ' Post. 0. none., m; Conv. of Alt. Int. ' Thm. Geometry Chpter 5
5 Answers for Lesson -, pp. 7 9 Eercises (cont.)... c. d. e. Conv. of Corr. '. The corr. ' he drws re C 7. m m 80 (Given). m m 80 ( Add. Post.). m m m m (Sustitution). m m (Sut. Prop. of )., n (Conv. of Corres. ' Post.) 8. 0; m m ; m m ; m m 0..5; m m 0. The corr. ' re, nd the ors re y the Conv. of Corr. ' Post.. Answers my vry. Smple: 9; j k y Conv. of the Alt. Int. ' Thm.. Answers my vry. Smple: 9; j k y Conv. of the Alt. Int.' Thm. nd, m y Conv. of Sme-Side Int. ' Thm. 5. Answers my vry. Smple: ;, m y Conv. of the Alt. Int. ' Thm. nd j k y Conv. of Corr. ' Post. 6. Answers my vry. Smple: nd re suppl.; j k y the Conv. of Corr. ' Post. 7. Vert. ' Thm. nd Conv. of Corr. ' Post. Geometry Chpter 55
6 Answers for Lesson -, pp. 7 9 Eercises (cont.) 8.., n. Given. 8. Corres. ' Post.. 8. Given.. Trns. Prop. of 5. j k 5. Conv. of Corres. ' Post. 9.. j k. Given. m 9 m 80. Sme-Side Int. ' Thm.. m 8 m Given 0.. m 9 m. Trns. Prop. of m 8 m 9 5. m m 8 5. Sut. Prop. of 6., n 6. Conv. of Corres. ' Post. nd re supp. Given m Conv. of Corr. Post. m m 80 Supp. Thm. Add. Post. nd re supp. Def. of suppl.. PL NA nd PN LA y Conv. of Sme-Side Int. ' Thm.. PL NA y Conv. of Sme-Side Int. ' Thm. Geometry Chpter 56
7 Answers for Lesson -, pp. 7 9 Eercises (cont.). none. PN LA y Conv. of Sme-Side Int. ' Thm. 5.. Answers my vry. Smple: e c A O B d X Z. Given: with trnsversl e, c isects AOB, d isects AXZ. c. Prove: c d d. To prove tht c d, show tht. if AOB OXZ. AOB OXZ y the Corr. ' Post. e.. (Given). AOB AXZ (Corr. ' Post.). m AOB m AXZ (Def. of '). m AOB m m ; m AXZ m m ( Add. Post.) 5. c isects AOB; d isects AXZ. (Given) 6. m m ; m m (Def. of isector) 7. m m m m (Trns. Prop. of ) 8. m m m m (Sust.) 9. m m (Add. Prop.) 0. m m (Div. Prop.). c d (Conv. of Corr. ' Post.) Geometry Chpter 57
8 Answers for Lesson -, pp. Eercises... Slt D is perp. to slts B nd C. Eplntions my vry. Smple: Slt D is perp. to slt A. Slts A, B, nd C re prllel, so y Theorem -, slt D is lso perp. to B nd C.. is perp. to nd c is perp. to, so is prllel to c ecuse two lines perp. to the sme line re prllel. d is prllel to c nd is prllel to c, so y Thm. -9, is prllel to d... corr. ',c., (ny order) d. Converse of Corr.. Answers my vry. Smples re given.. The rungs re prllel to ech other ecuse they re ll perpendiculr to the sme side. 5. All of the rungs re perpendiculr to one side. The side is perp. to the top rung, nd ecuse ll of the rungs re prllel to ech other, the side is perp. to ll of the rungs. 6. The rungs re perpendiculr to oth sides. The rungs re perp. to one of two prllel lines, so they re perp. to oth lines. 7. The rungs re prllel to ech other ecuse they re ll perpendiculr to one side. The sides re prllel ecuse they re oth perpendiculr to one rung. 8. The sides re prllel ecuse they re oth perpendiculr to one rung. 9. All of the rungs re prllel. All of the rungs re prllel to one rung, so they re ll prllel to ech other. Geometry Chpter 58
9 Answers for Lesson -, pp. Eercises 0. The rungs re prllel ecuse they re ll perpendiculr to one side.. In the digrm, # mens the mrked is rt.. c mens tht the corres. formed y nd c is rt., so # c.. Thm. -0. Answers my vry. Smple: In the digrm, AB # BH nd AB # BD, ut BH 6 BD. They intersect.. d 5. # d 6. # d 7. # d 8. d 9. d 0. d. # d. Refleive: ; flse; ny line intersects itself. Symmetric: If, then ; true; nd re coplnr nd do not intersect. Trnsitive: In generl, if, nd c, then c; true; however, when, nd, it does not follow tht.. Refleive: # ; flse; # lines re two lines tht intersect to form right '. Symmetric: If #, then # ; true; nd intersect to form right '. Trnsitive: If #, nd # c, then # c; flse; in plne, two lines # to the sme line re. Geometry Chpter 59
10 Answers for Lesson -, pp Eercises ; y 0; z ; y right, sclene 8. cute, equingulr, equilterl 9. otuse, isosceles 0.. Not possile; right will lwys hve one longest side opp. the right , 6, 8. nd for 5 nd for 6 nd for 8 c. They re vert. '. Geometry Chpter 60
11 Answers for Lesson -, pp Eercises (cont.) m 9; m 88. 7, y. 6, 8. 7; 55, 5, 90; right. 7; 7, 65, 78; cute 5. 8, y 6, z 90; ABD: 6, 90, 5; right; BCD: 90, 5, 8; right; ABC: 7, 5, 5; cute 6. 67, 58, c 5, d, e 90; FGH: 58, 67, 55; cute; FEH: 5,, ; otuse; EFG: 67,, 90; right 7. 60; Yes, n equilterl is isosc. ecuse if three sides of re, then t lest two sides re. No, the third side of n isosc. does not need to e to the other two. 9. eight Right isosceles 0. A. 0 nd , 60, 80. cute Otuse sclene Acute isosceles Right sclene Geometry Chpter 6
12 Answers for Lesson -, pp Eercises (cont.). Check students work. Answers my vry. Smple: The two et. ' formed t verte A re vert. ' nd thus hve the sme mesure.. By the definition of right ngle, m C 90. By the Tringle Angle-Sum Theorem, m A m B m C 80. Sutrcting 90 from ech side gives m A m B 90, so A nd B re complementry y the definition of comp. ngles. 5. m m 80 y the Add. Postulte. m m m 80 y the -Sum Theorem. m m m m m y the Trns. Property of Equlity. m m m y the Sutr. Property of Equlity. 6. ; since the third is 68, the lrgest et. is Check students work , 6, 7 c. cute 9... There re no such tringles c. isosceles tringle.. Answers my vry. Smple: The mesure of the et. is to the sum of the mesures of the two remote int. '. Since these ' re, the ' formed y the isector of the et. re to ech of them. Therefore, the isector is to the included side of the remote int. ' y the Conv. of the Alt Int. ' Thm. Geometry Chpter 6
13 Answers for Lesson -5, pp. 6 6 Eercises. yes. No; it hs no sides.. No; it is not plne figure.. No; two sides intersect etween endpoints. 5. MWBFX; sides: MW, WB, BF, FX, XM; ': M, W, B, F, X 6. KCLP; sides: KC, CL, LP, PK; ': K, C, L, P 7. HEPTAGN; sides: HE, EP, PT, TA, AG, GN, NH; ': H, E, P, T, A, G, N 8. pentgon; conve 9. decgon; concve 0. pentgon; concve , , 60,., 9. 08; 7. 50; 0 0, 0. 60; ; , 5, C 7. octgon; m 5; m 5 90 Geometry Chpter 6
14 Answers for Lesson -5, pp. 6 6 Eercises (cont.) 8. If you solve 0, you get n 7.. This numer is not n integer ; ; 5. ; 0. 6; 0. 50;. 80 ; n 80. (n )80 c. 80n 80(n ) 60 d. Polygon Et. -Sum Thm. 7. y 0; z 70; qud. 8. w 7, 59, y 9, z ; 9. 6, 7, 08, ; qud Answers my vry. Smples re given Yes; the sum of the mesures of ' t the int. point is 60. The sum of the mesures of ll the > is 80n. 80n 60 (n ) Answers my vry. Smple: The figure is conve equilterl qud. The sum of its ' is 80 or octgon (n )80 n Geometry Chpter 6
15 Answers for Lesson -5, pp. 6 6 Eercises (cont.) 57.. (0, 6), (0, 7), (60, 7), (80, 75.5), (00, 76.), (0, 77), (0, 77.), (60, 77.75), (80, 78), (00, 78.). 8 Interior Angle Mesure of Regulr Polygons c. It is very close to 80. d. No, two sides cnnot e colliner [80(n )] n Interior Angle Mesure n n 60 n 5. As n gets lrger, the size of the ngles get closer to 80. The more sides it hs, the closer the polygon is to circle Answers my vry. Smples re given. 60 n Not possile; opp. sides would overlp Not possile; opp. nd dj. sides would overlp. Geometry Chpter 65
16 Answers for Lesson -6, pp Eercises. y. y. 7 5 y O O O. y 5. y 6. O O 5 y 0 O 0 7. y 8. y 9. O 8 0. y. y. y O. y. y y O 5 y O y 6 y O 6 y O O O Geometry Chpter 66
17 Answers for Lesson -6, pp Eercises (cont.) 5. y 6. y y O O y 7. y ( ) 8. y ( ) 9. y 5 ( ) 0. y 6 ( ). y ( 6). y ( 0) or y 8. Equtions my vry from the pt. chosen. Smples re given.. y 5 ( 0). y ( 6) 5. y 6 ( ) 6. y ( ) 7. y 0 ( ) 8. y 0 ( 8) 9.. y y.... y.. y y. y 5. O 5 O 6 O 6 y 6 6. y y O O Geometry Chpter 67
18 Answers for Lesson -6, pp Eercises (cont.) the cost per min c..95 d. the initil chrge for cll 9. No; line with no slope is verticl line. 0 slope is horizontl line. 0.. m 0; it is horizontl line.. y 0.. Undefined; it is verticl line.. 0. Answers my vry. Smples re given.. The eq. is in stndrd form; chnge to slope-intercept form, ecuse it is esy to grph the eq. from tht form.. The eq. is in slope-int. form; use slope-int. form, ecuse the eq. is lredy in tht form.. The eq. is in point-slope form; use point-slope form, ecuse the eq. is lredy in tht form. 5. y 6. O The slopes re the sme, nd the y-intercepts re different. 7. Check students work. O y The slopes re ll different, nd the y-intercepts re the sme. Geometry Chpter 68
19 Answers for Lesson -6, pp Eercises (cont.) 8. O y (6, ) y 50. y 5. y (, ) O y 0 y 0 O (0, 0) y 6 y 5 O (, 5) , 0.08; 0 ; it is possile only if the rmp zigzgs. 5. The y-intercepts re the sme, nd the lines hve the sme steepness. One line rises from left to right while the other flls from left to right. 5. Answers my vry. Smple: 5, y 6 ( 5), y 55. (, 0), (0, ); m 0 y 0 ( ), y or y y 0 ( 0) or y 5 0. y 5 ( ) or y 0 c. The s. vlue of the slopes is the sme, ut one slope is pos. nd the other is neg. One y-int. is t (0, 0) nd the other is t (0, 0). 57. Yes; the slope of AB the slope of BC. 58. No; the slope of DE the slope of EF. 59. Yes; the slope of GH the slope of HI. 5 5 Geometry Chpter 69
20 Answers for Lesson -6, pp Eercises (cont.) 60. Yes; the slope of JK the slope of KL. 6. y ( ); y 8 6. y 5 ( 5); y 5 6. y 6 ( ); y Geometry Chpter 70
21 Answers for Lesson -7, pp Eercises. Yes; oth slopes.. No; the slope of, nd the slope of,.. No; the slope of,, nd the slope of,.. Yes; oth slopes. 5. Yes; oth slopes Yes; the lines oth hve slope of ut different y-intercepts. 7. Yes; the lines oth hve slope of ut different y-intercepts. 8. Yes; the lines oth hve slope of ut different y-intercepts. 9. No; one slope 7 nd the other slope No; one slope nd the other slope.. Yes; the lines oth hve slope of 5 ut different y-intercepts.. y ( 0) or y. y 0 ( 6) or y ( 6). y ( ) 5. y ( 6) 6. Yes; the slope of,, nd the slope of, ;. 7. Yes; the slope of,, nd the slope of, ;. 8. No; the slope of,, nd the slope of, 5; Yes; the slope of,, nd the slope of, ;. Geometry Chpter 7
22 Answers for Lesson -7, pp Eercises (cont.) 0. Answers my vry. Smples re given. 0. y 6 ( 6). y ( ). y ( ). y. y 5. Yes; ( ). 6. Yes; one is verticl nd the other is horizontl. 7. No; Q. 8. A 7 7 R 9. slope of AB slope of CD ; AB CD slope of BC slope of AD ; BC AD 0. slope of AB slope of CD ; AB CD slope of BC slope of AD ; BC AD. slope of AB ; slope of CD ; AB slope of BC ; slope of AD ; BC. slope of AB slope of CD 0; AB CD slope of BC nd slope of AD ; BC. Answers my vry. Smple: y 5, y 5. No; two lines with the sme y-intercept re the sme line. 5. RS nd VU re horizontl with slope 0; RS VU; slope of RW slope of UT ; RW UT; slope of WV slope of ST ; WV ST 6. No; ecuse no pirs of slopes hve product of. 7. The lines will hve the sme slope CD 6 AD 6 AD 5 Geometry Chpter 7
23 Answers for Lesson -7, pp Eercises (cont.) 8. When lines re #, the product of their slopes is. So, two lines # to the sme line must hve the sme slope. 9.. y 0 ( 5). ecuse you re given point nd cn quickly find the slope 0.. #. neither. #. # 5. AC: d "(7 9) ( ) "0 BD: d "( ) (7 5) "0 AC BD 6. slope of AC 5; slope of BD 5; since 5 5, AC ' BD; midpoint AC (8, 6); midpoint BD (8, 6); since the midpoints re the sme, the digonls isect ech other. 7.. Answers my vry. Smple: y O c. The other possile loctions for S re (, ) nd (8, 7). 8. y 5 ( ) 6 R Q P S (6, ) 6 Geometry Chpter 7
24 Answers for Lesson -8, pp Eercises.. J A B J A,,.. J * AB ) B A AB B A B J 5 7. Constructions my vry. Smples using the following segments re shown:, AB, AB , A ' P * AB ) B Geometry Chpter 7
25 Answers for Lesson -8, pp Eercises (cont.) A P, ' B * AB ) P, ' R * RS ) S.. P S, ', '.. R < ' 5. Construct lt. int. ; then drw the line. 6.. P R R * RS ) * RS ) S P m A * RS ) S B C Geometry Chpter 75
26 Answers for Lesson -8, pp Eercises (cont.) 7. Constructions my vry. Smples re given c c m The sides re nd. c. Check students work... c c Geometry Chpter 76
27 Answers for Lesson -8, pp Eercises (cont.). c. c d. The sides of the smller re hlf the length of the sides of the lrger tht they re to. e. Check students work. 5. D 6.. Check students work. c. p m; in plne, two lines # to third line re Answers my vry. Smples re given D G D D G G The qud. is rectngle. The qud. is squre Geometry Chpter 77
28 Answers for Lesson -8, pp Eercises (cont.).... c c c c 5. Not possile; if c, then c or c. The smller sides would meet t the midpoint of the longer side, forming segment. 6. Not possile; the smller sides would meet t the midpoint of the longer side, forming segment. Geometry Chpter 78
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