SSS/SAS/ASA Proofs

1. SSS/SAS/ASAProofs

2. C ! 1 2 A B D

3. Quiz Question W ! 3 4 Y Z X

4. ! G I H J F K L

5. C ! A 1 D 2 B

6. M ! R N O

7. ! B E C 1 2 A D

8. Quiz Question ! N Q 4 5 O P M

9. C 1 2 B A D E

10. G H 1 2 F E C B D

11. B E C 1 2 A D

12. B D F 1 2 A C 3 4 E

13. A X Y 1 3 B 2 4 C

14. A X Y 1 3 2 4

15. S 3 1 X R T 2 4 U

16. C D 1 2 3 4 A B Y

17. E F G C D A B

18. S R Q P T

19. Quiz Question E B C D A

20. Given as homework

21. B A C Hw 11.3 D

22. A C E B Hw 11.3 D

23. F G D E A B C Hw 11.4

24. U T S W V R Hw 11.4

25. N R Hw 11.5 M S P Q

26. B D A C Hw 11.5

27. A Hw 11.6 1 2 3 4 B M C

28. QUIZ Z Y 2 3 4 1 W X

30. Triangle Congruence and Similarity Proofs Augustus Vitug Melissa Moize

31. Sketch AB  AC BD  DC AD  AD BAD  CAD Proof Title: Statement Reason • Given • Given • Reflexive property • SSS •  Given AB  AC BD  DC Prove BAD  CAD

32. Sketch ABC DCB CB  BC DBC  ACB ABC  DCB CA  DB AB  CD Proof Title: Statement Reason • Alt. Int. ’s • reflexive • Alt. Int. ’s • ASA • CPCTC • CPCTC •  Given ABCD Prove AC  BD CD  AB

33. Sketch ABC  DCB CB  BC DBC  ACB  ABC   DCB AB  CD ADC  BAD  ABE  DCF AE DE BECE Proof Title: Parallelogram Diagonals Bisect Each Other Statement Reason • Alt. Int. ’s • Reflexive property • Alt. Int. ’s • ASA • CPCTC • Alt. Int. ’s • ASA • CPCTC • CPCTC Given ABCD Prove AEDE BECE

34. Sketch ABC  DCB CB  BC ACB  DBC ABC  DCB A  D ABC + DBC  DCB +ACB Proof Title: Statement Reason • Alt. Int. ’s • reflexive • Alt. Int. ’s • ASA • CPCTC • 2nd Postulate •  Given Prove A  D ABD  DCA

35. Sketch ABC DCB CBBC CBD BCA ABC  DCB FBD+BFD+BDF  ECA+CEA+CAE BDF CAE AEFD ACBD BFD  CEA CE BF EF  FE EF+FB  FE+EC EB  CF AB  CD AEFD CFD  BEA Proof Title: Compound Polygon #1 Statement Reason • Alt. int. ’s • reflexive property • Alt. int. ’s • ASA • Triangle Sums • Subtraction Property • Given • CPCTC • ASA • CPCTC • Reflexive Property • Sums of equals • Sums of equals • CPCTC • Given • SSS Given ABCD AEFD AEC=90 BFD=90 Prove CFD  BEA

36. Sketch AC BD ACD BDC CD  DC ADC  BDC CE+BE  DE+AE CE  DE CED is isos Proof Title: Compound # 2 Statement Reason • Given • Def. isos • Reflexive • SAS • Sums of Equals • Subtraction property • def. isos. Given ABCD is iso. Prove CED is isos

37. Sketch AB  CD B  D BE  DE BEA  DEC G   H EC  EA FE  XE FEA  XEC AF  CX Proof Title: ? Statement Reason • Given • Given • Def. of Midpoint • SAS • CPCTC • CPCTC • Def. of Midpoint • SAS • CPCTC Given AB  CD B  D E is the midpoint of BD & FX Prove AF  CX

38. Sketch AECE DEC  BEA BE DE AEB  CED ABE  CDE ABE,CDE are alt. int. ’s AB || DC Proof Title: Simple Bowtie Statement Reason • Def. Bisector • Vertical ’s • Def. Bisector . • SAS • CPCTC • Def. Alt. Int. ’s •  Alt. Int. ’s are congruent Given Line AC bis. Line BD Prove AB || CD

39. Sketch A  D BC  FE B = 90- A  E = 90- D B  E ABC  DEF BA  DE Proof Title: Statement Reason • given • given • difference of equals • - property • ASA • CPCTC •  Given ABC is a Right  BC  FE A  D Prove BA  DE

40. Sketch AGE+EGB CGF+ FGD AGB  CGD FGD  EGB ABGCDG DFG  BEG Proof Title: Compound Bowtie #1 Statement Reason • Given • Vertical ’s • Given • SAS • Vertical ’s • Given • Alt. Int. ’s • ASA • CPCTC •  Given Prove

41. Sketch AED  BEC DE  CE ADC-EDC  BCD ECD ADE  BCE ADE  BCE AD  BC ADC   BCD DC  CD ADC  BCD Proof Title: Statement Reason • Vertical ’s • Def. iso.  • Dif. Of equals • Sub. Prop. • ASA • CPCTC • Sum of Equals • Reflexive Prop. • SAS •  Given EDC is isosceles Prove ADC  BCD

42. Sketch AE  BE AED  BEC DE  CE ADE  BCE FDE  GCE DECE FED  GEC FD  GC EDC  ECD ADE+EDC  BCE+ ECD ADCBCD FGDC Proof Title: Statement Reason • Given • Vert. ’s • def. iso.  • SAS • CPCTC • def. iso.  • alt. int. ’s • CPCTC • Def. iso.  • Addition prop. Of equality •  Given AEBE EDC is isosceles Prove FG DC

43. Sketch AC  BD ACD  BDC CD  DC  ACD   BDC AD  BC Proof Title: Diagonals of a Rectangle Statement Reason • Dfn. Rectangle • Dfn. Rectangle • Reflexive • SAS • CPCTC •  Given Rectangle ABCD Prove AD  BC

44. Sketch BAM  CAM ABAC B C BAM  CAM BM  CM BMA  CMA BMC  180 BMA = 1/2180=90= CMA AM  bis. Of BC Proof Title: Statement Reason •  bis. • Given • Def. iso.  • ASA • CPCTC • CPCTC • straight ’s • Angle Addition Given ABC w/ AM  bis. ABAC Prove AM bis.

45. Sketch ¾=5/6.6666 AD/AB=AE/AC A  A ADE  ABC Proof Title: Statement Reason • 36&2/3=4  5= 20 • CPSTP • Reflexive • SAS Given DE || BC Prove ADE  ABC

46. Sketch AEBE BEDAEC CE  DE AC  BD Proof Title: Simple butterfly Statement Reason • Given • Vertical angels • Given • CPCTC Given AEBE CEDE Prove AC  BD

47. Sketch BCA  EFD FC  CF AF  CD AF + FC  DC + CF ABC  DEF Proof Title: Statement Reason • Alt. Int. ’s • Reflexive • Given • Addition • ASA •  Given AF  DC FE || CB AB || DE Prove ABC  DEF

48. Sketch BG  EG EG + GF=BG+GC BC  EF FC  FC AF+FC=DC+CF GFC  GCF AC=CD ABC  DEF Proof Title: Statement Reason • Given • Sum’s of =‘s • Segment addition • reflexive • Sum’s of =‘s • def. isosceles  • Segment Addition • SAS •  Given FGC Isosceles AF  DC BG  EG Prove ABC  DEF

49. Sketch BM  CM AMB = 90 = AMC AB  AC B  C BAM  CAM BAM   CAM AM is  bis. of A Proof Title: Isos. Triangle  to  bisector Statement Reason • Def.  bis. • Def.  bis. • given • def. isos. triangle • SAS • CPCTC •  • Given • ABC is isos. AB  AC AM is  Prove  bis. of BC is  bis. Of A

50. Sketch BMA=90= CMA B  C B+ BMA+ BAM=180 C+ CMA+ CAM =180 B+ BMA+ BAM= C+ CMA+ CAM BAM  CAM  AM is bis. of A Proof Title: Statement Reason • Def. Alt. • isos triangle •  sums •  sums • transitive • - property •  Given ABC is isos. AC  AB AM is Alt. Prove Alt. AM is  bis. of A