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Proving Triangles Congruent

Proving Triangles Congruent. F. B. A. C. E. D. The Idea of a Congruence. Two geometric figures with exactly the same size and shape. Corresponding Parts. AB  DE BC  EF AC  DF  A   D  B   E  C   F. B. A. C. E. F. D.

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Proving Triangles Congruent

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  1. Proving Triangles Congruent

  2. F B A C E D The Idea of a Congruence Two geometric figures with exactly the same size and shape.

  3. Corresponding Parts • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F B A C E F D Definition of Congruent Triangles: if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF

  4. SSS SAS ASA AAS Do you need all six ? NO !

  5. Side-Side-Side (SSS) E B F A D C • AB DE • BC EF • AC DF ABC DEF

  6. Side-Angle-Side (SAS) B E F A C D • AB DE • A D • AC DF ABC DEF included angle

  7. Included Angle The angle between two sides H G I

  8. E Y S Included Angle Name the included angle: YE and ES ES and YS YS and YE E S Y

  9. Angle-Side-Angle (ASA) B E F A C D • A D • AB  DE • B E ABC DEF included side

  10. Included Side The side between two angles GI GH HI

  11. E Y S Included Side Name the includedside: Y and E E and S S and Y YE ES SY

  12. Angle-Angle-Side (AAS) B E F A C D • A D • B E • BC  EF ABC DEF Non-included side

  13. Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT

  14. Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C F D NOT CONGRUENT

  15. SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • SSA correspondence • AAA correspondence The Congruence Postulates

  16. Name That Postulate (when possible) SAS ASA SSA SSS

  17. Name That Postulate (when possible) AAA ASA SSA SAS

  18. SSA Name That Postulate (when possible) Vertical Angles Reflexive Property SAS SAS Reflexive Property Vertical Angles SAS

  19. HW: Name That Postulate (when possible) sss None None None

  20. HW: Name That Postulate (when possible) None ASA SAS

  21. Let’s Practice ACFE Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AF For AAS:

  22. More Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. N V For ASA: MKTU For SAS: For AAS: MU

  23. This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.

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