Geometry unit 4.1 4.3
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The document discusses congruence postulates for triangles. It explains that two triangles are congruent if they meet the criteria of Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS). The document provides examples of applying these postulates to determine if triangles are congruent and identifies the additional information needed.
Geometry unit 4.1 4.3
- 3. TThhee IIddeeaa ooff aa CCoonnggrruueennccee Two geometric figures with exactly the same size and shape. B A C F E D
- 4. HHooww mmuucchh ddoo yyoouu nneeeedd ttoo kknnooww.. .. .. . . . about two triangles to prove that they are congruent?
- 5. CCoorrrreessppoonnddiinngg PPaarrttss You learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. B A C DABC @ D DEF E D F 1. AB @ DE 2. BC @ EF 3. AC @ DF 4. Ð A @ Ð D 5. Ð B @ Ð E 6. Ð C @ Ð F
- 6. DDoo yyoouu nneeeedd aallll ssiixx ?? NO ! SSS SAS ASA AAS
- 7. SSiiddee--SSiiddee--SSiiddee ((SSSSSS)) 1. AB @ DE 2. BC @ EF 3. AC @ DF DABC @ D DEF B A C E D F
- 8. SSiiddee--AAnnggllee--SSiiddee ((SSAASS)) 1. AB @ DE 2. ÐA @ Ð D 3. AC @ DF DABC @ D DEF B A C E D F included angle
- 9. IInncclluuddeedd AAnnggllee The angle between two sides Ð G Ð I Ð H
- 10. IInncclluuddeedd AAnnggllee Name the included angle: YE and ES ES and YS YS and YE E Y S Ð E Ð S Ð Y
- 11. AAnnggllee--SSiiddee--AAnnggllee ((AASSAA)) 1. ÐA @ Ð D 2. AB @ DE 3. Ð B @ Ð E DABC @ D DEF B A C E D F included side
- 12. IInncclluuddeedd SSiiddee The side between two angles GI HI GH
- 13. IInncclluuddeedd SSiiddee Name the included side: ÐY and ÐE ÐE and ÐS ÐS and ÐY E Y S YE ES SY
- 14. AAnnggllee--AAnnggllee--SSiiddee ((AAAASS)) 1. ÐA @ Ð D 2. Ð B @ Ð E 3. BC @ EF DABC @ D DEF B A C E D F Non-included side
- 15. WWaarrnniinngg:: NNoo SSSSAA PPoossttuullaattee B There is no such thing as an SSA postulate! A C E D F NOT CONGRUENT
- 16. WWaarrnniinngg:: NNoo AAAAAA PPoossttuullaattee B A C E D F There is no such thing as an AAA postulate! NOT CONGRUENT
- 17. TThhee CCoonnggrruueennccee PPoossttuullaatteess SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence
- 18. NNaammee TThhaatt PPoossttuullaattee (when possible) SSAASS AASSAA SSSSAA SSSSSS
- 19. NNaammee TThhaatt PPoossttuullaattee (when possible) AASSAA AAAAAA SSAASS SSSSAA
- 20. NNaammee TThhaatt PPoossttuullaattee (when possible) Reflexive SSAASS SSAASS SSAASS Property Vertical Angles Vertical Angles Reflexive Property SSSSAA
- 21. HHWW:: NNaammee TThhaatt PPoossttuullaattee (when possible)
- 22. HHWW:: NNaammee TThhaatt PPoosstt(uuwhlleaan pttoseesible)
- 23. LLeett’’ss PPrraaccttiiccee Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: ÐB @ ÐD AC @ FE For AAS: ÐA @ ÐF
- 24. HHWW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:
- 25. A B F C E D
- 26. Slide 1 of 2
- 27. Slide 1 of 2
- 28. Before we start…let’s get a few things straight A B Y INCLUDED SIDE C X Z
- 29. Angle-Side-Angle (ASA) Congruence Postulate Two angles and the INCLUDED side
- 30. Angle-Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included
- 31. }Your Only Ways To Prove Triangles Are Congruent
- 32. Things you can mark on a triangle when they aren’t marked. Overlapping sides are congruent in each triangle by the REFLEXIVE property Vertical Angles are congruent Alt Int Angles are congruent given parallel lines
- 33. ΔDEF ΔLMN Ð D @ Ð N DE @ NL Ð @ Ð In and , , and E L . Write a congruence statement. D D E F @ D N L M
- 34. What other pair of angles needs to be marked so that the two triangles are congruent by AAS? F D E M L N ÐE @ ÐN
- 35. What other pair of angles needs to be marked so that the two triangles are congruent by ASA? F D E M L N ÐD @ ÐL
- 36. ΔGIH @ ΔJIK by AAS G I H J K Ex 4
- 37. B A ΔABC @ ΔEDC by ASA C D E Ex 5
- 38. ΔACB @ ΔECD by SAS B A C E D Ex 6
- 39. J K M L ΔJMK @ ΔLKM by SAS or ASA Ex 7
- 40. Not possible K J L T U Ex 8 V
- 41. Slide 2 of 2
- 42. Slide 2 of 2
- 43. Slide 2 of 2
- 44. Slide 2 of 2
- 45. (over Lesson 5-5) Slide 1 of 2
- 46. (over Lesson 5-5) Slide 1 of 2
- 47. Slide 1 of 2
- 48. Slide 1 of 2
- 49. Slide 1 of 2
- 50. Slide 1 of 2
- 51. Slide 2 of 2
- 52. Slide 2 of 2
- 53. Slide 2 of 2
- 54. Slide 2 of 2
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