Congruence in Right Triangles GEOMETRY LESSON 4-6 Pages 219-223 Exercises 1. ABC DEF by HL. Both are rt. , AC DF, and CB FE. 2. SPR QRP by HL. Both are rt. , SP QR (given) and PR PR by the Reflexive Prop. of . 3. LMP OMN by HL. Both are rt. because vert. are ; LP NO, and LM OM. s 4. AEB DCB by HL. Both are rt. . AB BD and EB CB by the def. of midpt. 5. T and Q are rt. . 6. RX RT or XV TV 7. TY ER or RT YE 8. Right are needed, either A and G or AQC and GJC. s 9. BC FA 10. RT NQ 11. a. Given b. Def. of rt. c. Reflexive Prop. of d. Given e. HL 4-6

Congruence in Right Triangles GEOMETRY LESSON 4-6 12. a. suppl. are rt. b. Def. of rt. c. Given d. Reflexive Prop. of e. HL 13. PS PT so S T by the Isosc. Thm. PRS PRT. PRS PRT by AAS. 14. Yes; RS TU and RT TV. s 15. Yes; PM PM and PMW is a rt. since JP || MW. 16. a. Given b. Def. of c. MLJ and KJL are rt. . d. Given e. LJ LJ f. HL s 17. a. Given b. IGH c. Def. of rt. d. I is the midpt. of HV. e. Def. of midpt. f. IGH ITV 18. HL; each rt. has a hyp. and side. 19. x = 3; y = 2 20. x = –1; y = 3 4-6

Congruence in Right Triangles GEOMETRY LESSON 4-6 21. whether the 7-yd side is the hyp. or a leg 22. ABX ADX; HL ABC ADC; SSS or SAS BXC DXC; HL 23. a. Answers may vary. Sample: You could show that suppl. AXB and AXD are . b. ABC ADC by SSS so BAC DAC by CPCTC. ABX ADX by SAS so AXB AXD. AXB is suppl. and to AXD so they are both rt. . s 24. 25. 26. 27. 4-6

Congruence in Right Triangles GEOMETRY LESSON 4-6 28. 1. EB DB; A and C are rt. (Given) 2. BEA BDC are rt. (Def. of rt. ) 3. B is the midpt. of AC (Given) 4. AB BC (Def. of midpt.) 5. BEA BDC (HL) s 29. 1. LO bisects MLN, OM LM, ON LN, (Given) 2. M and N are rt. (Def. of ) 3. MLO NLO (Def. of bis.) 4. M N (All rt. are .) 5. LO LO (Reflexive Prop. of ) 6. LMO LNO (AAS) s 30. Answers may vary. Sample: Measure 2 sides of the formed by the amp. and the platform’s corner. Since the will be by HL or SAS, the are the same. s 4-6

Congruence in Right Triangles GEOMETRY LESSON 4-6 31. a. b. slope of DG = –1; slope of GF = –1; slope of GE = 1 c. EGD and EGF are rt. . d. DE = 26 ; FE = 26 s 31. (continued) e. EGD EGF by HL. Both are rt. , DE FE, and EG EG. 32. An HA Thm. is the same as AAS with AAS corr. to the rt. , an acute , and the hyp. s 33. Since BE EA and BE EC, AEB and CEB are both rt. . AB BC because ABC is equilateral, and BE BE. AEB CEB by HL. 34. No; AB CB because AEB CEB, but doesn’t have to be to AB or to CB. 35. A 36. H s 4-6

Congruence in Right Triangles GEOMETRY LESSON 4-6 37. D 38. [2] a. TFW TGW b. RFW and RGW are rt. . [1] one part correct 39. isosceles 40. equilateral s 41. BC || AD because each slope = –1. BT BA, BA AD because product of slopes is –1. 42. If || lines then alt. int. are . 43. If two lines are ||, then same-side int. are suppl. 44. Vert. are . 45. If two lines are ||, then corr. are . s 46. If two lines are ||, then corr. are . 47. If two lines are ||, then same-side int. are suppl. s 4-6