Geometrycongruence

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Proving Triangles Congruent

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Geometrycongruence

  1. 1. Proving TrianglesCongruent
  2. 2. Two geometric figures withexactly the same size andshape.The Idea of a CongruenceThe Idea of a CongruenceA CBDEF
  3. 3. How much do youHow much do youneed to know. . .need to know. . .. . . about two trianglesto prove that theyare congruent?
  4. 4. In Lesson 4.2, you learned that if allsix pairs of corresponding parts (sidesand angles) are congruent, then thetriangles are congruent.Corresponding PartsCorresponding Parts∆ABC ≅ ∆DEFBACEDF1. AB ≅ DE2. BC ≅ EF3. AC ≅ DF4. ∠ A ≅ ∠ D5. ∠ B ≅ ∠ E6. ∠ C ≅ ∠ F
  5. 5. Do you needDo you need all six ?all six ?NO !SSSSASASAAAS
  6. 6. Side-Side-Side (SSS)Side-Side-Side (SSS)1. AB ≅ DE2. BC ≅ EF3. AC ≅ DF∆ABC ≅ ∆ DEFBACEDF
  7. 7. Side-Angle-Side (SAS)Side-Angle-Side (SAS)1. AB ≅ DE2. ∠A ≅ ∠ D3. AC ≅ DF∆ABC ≅ ∆ DEFBACEDFincludedangle
  8. 8. The angle between two sidesIncluded AngleIncluded Angle∠ G ∠ I ∠ H
  9. 9. Name the included angle:YE and ESES and YSYS and YEIncluded AngleIncluded AngleSYE∠ E∠ S∠ Y
  10. 10. Angle-Side-Angle-Side-AngleAngle (ASA)(ASA)1. ∠A ≅ ∠ D2. AB ≅ DE3. ∠ B ≅ ∠ E∆ABC ≅ ∆ DEFBACEDFincludedside
  11. 11. The side between two anglesIncluded SideIncluded SideGI HI GH
  12. 12. Name the included angle:∠Y and ∠E∠E and ∠S∠S and ∠YIncluded SideIncluded SideSYEYEESSY
  13. 13. Angle-Angle-Side (AAS)Angle-Angle-Side (AAS)1. ∠A ≅ ∠ D2. ∠ B ≅ ∠ E3. BC ≅ EF∆ABC ≅ ∆ DEFBACEDFNon-includedside
  14. 14. Warning:Warning: No SSA PostulateNo SSA PostulateA CBDEFNOT CONGRUENTThere is no suchthing as an SSApostulate!
  15. 15. Warning:Warning: No AAA PostulateNo AAA PostulateA CBDEFThere is no suchthing as an AAApostulate!NOT CONGRUENT
  16. 16. The Congruence PostulatesThe Congruence PostulatesSSS correspondenceASA correspondenceSAS correspondenceAAS correspondenceSSA correspondenceAAA correspondence
  17. 17. Name That PostulateName That PostulateSASSASASAASASSSSSSSSASSA(when possible)
  18. 18. Name That PostulateName That Postulate(when possible)ASAASASASSASAAAAAASSASSA
  19. 19. Name That PostulateName That Postulate(when possible)SASSASSASSASSASSASReflexivePropertyVerticalAnglesVerticalAnglesReflexiveProperty SSASSA
  20. 20. HW: Name That PostulateHW: Name That Postulate(when possible)
  21. 21. (when possible)HW: Name That PostulateHW: Name That Postulate
  22. 22. Let’s PracticeLet’s PracticeIndicate the additional information neededto enable us to apply the specifiedcongruence postulate.For ASA:For SAS:∠B ≅ ∠DFor AAS: ∠A ≅ ∠FAC ≅ FE
  23. 23. HWHWIndicate the additional information neededto enable us to apply the specifiedcongruence postulate.For ASA:For SAS:For AAS:
  24. 24. This powerpoint was kindly donated towww.worldofteaching.comhttp://www.worldofteaching.com is home to over athousand powerpoints submitted by teachers. This is acompletely free site and requires no registration. Pleasevisit and I hope it will help in your teaching.

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