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Proving Triangles Congruent

Learn about the different ways to prove triangles congruent - SAS, SSS, ASA, AAS, and HL. Explore the idea of corresponding parts and the need for additional information.

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Proving Triangles Congruent

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  1. Proving Triangles Congruent Free powerpoints at http://www.worldofteaching.com

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

  3. How much do you need to know. . . . . . about two triangles to prove that they are congruent?

  4. Corresponding Parts • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F B A C E F D In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF

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

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

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

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

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

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

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

  12. E Y S Included Side Name the included side: Y and E E and S S and Y YE ES SY

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

  14. Hypotenuse-Leg (HL) B F E A C D • BA DF • BC  ED ABC FDE Leg Hypotenuse

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

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

  17. The Congruence Postulates • SSS • ASA • SAS • AAS • HL • SSA • AAA

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

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

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

  21. Name That Postulate (when possible)

  22. Name That Postulate (when possible)

  23. 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:

  24. Partner Excercise Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

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