1. Congruence in Right Triangles
GEOMETRY LESSON 4-6
Pages 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
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2. 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
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3. Congruence in Right Triangles
GEOMETRY LESSON 4-6
21. whether the 7-yd side is the hyp. or a leg
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.
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4. Congruence in Right Triangles
GEOMETRY LESSON 4-6
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
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
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5. 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 = ; 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
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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
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