Midsegments of Triangles GEOMETRY LESSON 5-1 Pages 246-248 Exercises 1. 9 2. 7 3. 14 4. 23 5. 11 6. 2 7. 40 8. 50 9. 160 10. 80 11. UW TX; UY VX; YW TV 12. GJ FK; JL HF; GL HK 13. a. ST PR; SU QR; UT PQ b. m QPR = 40 14. FE 15. FG 16. AB 17. EG 18. AC 19. CB 20. a. 1050 ft. b. 437.5 ft. 1 2 5-1

Midsegments of Triangles GEOMETRY LESSON 5-1 21. a. 114 ft. 9 in. b. Answers may vary. Sample: The highlighted segment is the midsegment of the triangular face of the building. 22. 60 23. 45 24. 100 25. 55 26. a. H(2, 0); J(4, 2) 26. (continued) b. Slope of HJ = = 1; Slope of EF = = 1; therefore HJ EF. c. HJ = 22 + 22 = 8 = 2 2 ; EF = 42 + 42 = 32 = 4 2 ; therefore HJ = EF. 27. 18 28. 37 29. 60 2 4 1 5-1

Midsegments of Triangles GEOMETRY LESSON 5-1 30. 50 31. 10 32. x = 6; y = 6 33. 154 cm 34. 52 35. x = 3; DF = 24 36. x = 9; EC = 26 37. Answers may vary. Sample: Draw CA and extend CA to P 37. (continued) so that CA = AP. Find B, the midpt. Of PD. Then, by the Midsegment Thm., AB CD and AB = CD. 38. G(4, 4); H(0, 2); J(8, 0) 39. UTS; Proofs may vary; Sample: VS SY, YT TZ, and VU UZ because S, T, and U are midpts. of the respective sides; ST = VZ so ST VU UZ; SU = YZ so SU YT TZ; and TU = VY so TU SY SV; therefore YST TUZ SVU UTS by SSS. 1 2 1 2 1 2 1 2 1 2 5-1

Midsegments of Triangles GEOMETRY LESSON 5-1 40. 248 41. 174 42. 418 43. 70 44. 40 45. 70 46. 40 47. SXT TYS; SAS y = x + 2 y = 3x – 2 51. 48. ADC EBC; ASA 49. KLQ PNR; HL 50. 5-1

Midsegments of Triangles GEOMETRY LESSON 5-1 52. y = –x – 5 53. 46 54. 35 55. 40 2 3 5-1