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Notes 4.1-4.3 Triangle Congruence

Notes 4.1-4.3 Triangle Congruence Learning Targets I can recognize congruent figures and their corresponding parts. I can prove triangles congruent using SSS and SAS. I can prove triangles congruent using ASA and AAS. Congruence.

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Notes 4.1-4.3 Triangle Congruence

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  1. Notes 4.1-4.3 Triangle Congruence Learning TargetsI can recognize congruentfigures and their corresponding parts. I can prove triangles congruent using SSS and SAS. I can prove triangles congruent using ASA and AAS.

  2. Congruence Two geometric figures with exactly the same size and shape.

  3. Corresponding Parts B A C E F D If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Example 1 • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F ABC DEF

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

  5. Side-Side-Side or SSS

  6. Side-Side-Side (SSS) B A C E F • Example 1 • AB DE • BC EF • AC DF D ABC DEF

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

  8. Side-Angle-Side or SAS

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

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

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

  12. Angle-Side-Angle or ASA

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

  14. Angle-Angle-Side or AAS

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

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

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

  18. SSS • ASA • SAS • AAS • SSA • AAA The Congruence Postulates

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

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

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

  22. 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:

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