# Using Variables - Mrs. Powers' Class Bisectors in Triangles GEOMETRY GEOMETRY LESSON LESSON 5-2 5-2 Pages 251-254 Exercises 1. AC is the BD bis. of 7. y = 3; ST = 15; TU = 15 12. 5 13. 10 2. 3. 15 18 8. HL is the bis. of JHG because a point on HL is equidistant from J and G. 4. 8 5. The set of points equidistant from H and S is the bis. of HS. 9. y = 9; m FHL = 54; m KHL = 54 x = 12; JK = 17; JM =17 11. Point E is on the

bisector of KHF. 6. 10. 27 5-2 14. 10 15. Isosceles; it has 2 sides 16. equidistant; RT = RZ 17. A point on the bis. of a segment if and only if it is equidistant from the endpoints of the segment. Bisectors in Triangles GEOMETRY GEOMETRY LESSON LESSON 5-2 5-2 18. 12 19. 4 20. 4 21. 16 26. (continued) and CT = CY by the Bis. Thm. 31. The pitchers plate 32. a. 27. Answers may vary. Sample: the student needs to know that QS bisects PR. 22. 5 23. 10 28. No; A is not equidistant from the sides of X. 24. 7 29. Yes; AX bis.

TXR. 25. 14 26. Isosceles: CS = CT 30. Yes; A is equidistant from the sides of X. 5-2 b. The bisectors intersect at the same point. c. Check student's work. Bisectors in Triangles GEOMETRY GEOMETRY LESSON LESSON 5-2 5-2 33. a. 34-39. Answers may vary. Samples are given. 34. C(0, 2), D(1, 2); AC = BC = 2, AD = BD = 5 35. C(3, 2), D(3, 0); AC = BC = 3, AD = BD = 13 36. C(3, 0), D(3, 0); AC = BC = 3, AD = BD = 3 b. The bisectors intersect at the same point. 37. C(0, 0), D(1, 1); AC = BC = 3, AD = BD = c. Check students work 38. C(2, 2), D(4, 3);

AC = BC = 5, AD = BD = 5-2 2 5 10 Bisectors in Triangles GEOMETRY GEOMETRY LESSON LESSON 5-2 5-2 5 5 39. C 2 , 2 , D(5, 3); 26 AC = BC = , AD = BD = 2 40. a. 43. (continued) 13 : y = 3 x + 25 ; x = 10 4 5 b. (10, 5) c. CA = CB = 5 d. C is equidist. from OA and OB. 41. bisector; right; Reflexive; SAS; CPCTC 42. PQ; BAQ; CPCTC; bisector 43. Answers may vary. Sample: proof of the Conv. of the Bis. Thm. 5-2 Bisectors in Triangles GEOMETRY GEOMETRY LESSON

LESSON 5-2 5-2 44. x = 3 45. y = (x 2) 46. y = 1 x + 4 47. (continued) by A, B, and C and if it goes through the point that is the intersection of the bisectors of the sides of ABC. 2 47. 48. BP AB and PC AC, thus ABP and ACP are rt. s . Since AP bisects BAC, BAP Line is equidistant from points A, B, and C if it is to the plane determined CAP. AP AP by the Reflexive Prop. of . Thus ABP ACP by AAS and PB PC by CPCTC. Therefore, PB = PC. 5-2 Bisectors in Triangles GEOMETRY GEOMETRY LESSON LESSON 5-2 5-2 49. 1. SP QP; SR 2. QPS and 3. QPS QR QRS are rt.

QRS 1. Given s 2. Def. of 3. All rt. s are 4. SP = SR 4. Given 5. QS 5. Refl. Prop. of QS 6. QPS QRS 6. HL 7. PQS RQS 7. CPCTC 8. QS bisects PQR. 8. Def. of 5-2 bis .

Bisectors in Triangles GEOMETRY GEOMETRY LESSON LESSON 5-2 5-2 50. D 51. H 52. D 53.  Since MK MR, MK KV, and MR RV, the Bisector Thm. states that MV is the bisector of KVR. 54.  (continued) MRV are rt. s . By HL, MKV MRV. By CPCTC, KV RV. By the Converse of the Bisector Thm., points M and V lie on the bisector, so MV is the bisector of KR  appropriate steps with one logical error OR one incorrect reason statement  partially correct logical argument  two logical errors OR two incorrect reasons statements 54.  MK MR. By the Reflexive Prop. of , MV MV. It is given that MKV and  proved s but failed to reach desired conclusion 5-2 Bisectors in Triangles GEOMETRY GEOMETRY LESSON LESSON 5-2 5-2

55. 8 63. Trans. Prop. of 56. 4 64. C 3, 57. 6 65. C 0, 7 ; AB = 97, AC = BC = 97 58. Reflexive Prop. of = 66. C 11 , 5 ; AB = 17, AC = CB = 17 13 ; AB = 3 2 2 2 59. Div. Prop. of = 60. Add. Prop. of = 61. Distr. Prop. 62. Subst. or Transitive Prop. of = 5-2 5, AC = CB = 3 5 2 2 2