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1. (a) nI > nII > nIII, SAS; (b) nI > nIII, ASA; (c) nI > nII > nIII, SSS. 2. (a) ASA; (b) SAS; (c) SSS; (d) SAS; (e) ASA; ( f ) SAS; (g) SAS; (h) ASA. 3. (a) AD > DC; (b) jABD jDBC; (c) j1 > j4; (d) BE > ED; (e) BD > AC; ( f ) jBAD > jCDA 4. (a) j1 > j3, j2 > j4, BD > BE; (b) AB > AC, BD > DC, jB > jC; (c) jE > jC, jA > jF, jEDF > jABC 5. (a) x 19, y 8; (b) x 4, y 12; (c) x 48, y 12 8. (a) jb > jd, jE > jG; (b) jA > j1 > j4, j2 > jC; (c) j1 > j5, j4 > j6, jEAD > jEDA 9. (a) BE > EC; (b) AB > BD > AD, BC > CD; (c) BD > DE, EF > FC, AB > AC
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1. (a) x (e) x (i) x 2. (a) x 105 , y 75 ; (b) x 60 , y 40 ; (c) x 85 , y 95 ; (d) x 50 , y 50 ; 65 , y 65 ; ( f ) x 40 , y 30 ; (g) x 60 , y 120 ; (h) x 90 , y 35 ; 30 , y 40 ; ( j ) x 80 , y 10 ; (k) x 30 , y 150 ; (l) x 85 , y 95 22 , y 102 ; (b) x 40 , y 100 ; (c) x 80 , y 40
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3. (a) Each angle measures 105 . (b) Each angle measures 70 . (c) Angles measure 72 and 108 . 7. (a) 25; (b) 9; (c) 20; (d) 8 8. (a) 8; (b) 10; (c) 2; (d) 14 10. (a) P is equidistant from B and C. P is on bisector of BC. Q is equidistant from A and B. Q is on bisector of AB. R is equidistant from A, C, and D. R is on bisectors of AD and CD. (b) P is equidistant from AB and AD. P is on bisector of jA. Q is equidistant from AB and BC. Q is on bisector of jB. R is equidistant from BC, CD, and AD. R is on the bisectors of jC and jD. 11. (a) P is equidistant from AD, AB, and BC. Q is equidistant from AD and AB and equidistant from A and D. R is equidistant from AB and BC and equidistant from A and D. (b) P is equidistant from AD and CD and equidistant from B and C. Q is equidistant from A, B, and C. R is equidistant from AD and CD and equidistant from A and B. 12. (a) x (e) x 13. (a) x (e) x 50 , y 52 , y 55 , y 30 , y 110 ; (b) x 40 ; ( f ) x 125 ; (b) x 120 ; ( f ) x 65 , y 120 , y 80 , y 90 , y 65 ; (c) x 90 90 ; (c) x 30 30 , y 56 , y 100 ; (d) x 68 ; (d) x 51 , y 100 , y 112 ; 30 ;
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14. (a) 18 , 54 , 108 ; (b) 40 , 50 , 90 ; (c) 36 , 36 , 108 ; (d) 36 , 72 , 108 , 144 ; (e) 50 , 75 ; ( f ) 100 , 60 , and 20 16. (a) (b) (c) (d) Since x 45, each angle measures 60 . Since x 25, x 15 40 and 3x 35 40; that is, two angles each measure 40 . If 2x, 3x, and 5x represent the angles, x 18 and 5x 90; that is, one of the angles measures 95 . If x and 5x 10 represent the unknown angles, x 21 and 5x 10 95; that is, one of the angles measures 95 .
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17. (a) 7 st. , 30 st. ; (b) 1620 , 5400 , 180,000 ; (c) 30, 12, 27, 202 18. (a) 20 , 18 , 9 ; (b) 160 , 162 , 171 ; (c) 3, 9, 20, 180; (d) 3, 12, 36, 72, 360 19. (a) 65 , 90 , 95 , 110 ; (b) 140 , 100 , 60 , 60 20. (a) nI > nIII by hy-leg; (b) nI > nIII by SAA.
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