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Triangle Congruence Postulates and Theorems

Learn about Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates in triangle congruence. Understand why SSA and AAA postulates do not work. Practice identifying congruence postulates with examples. Complete a homework packet on ASA and AAS theorems.

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Triangle Congruence Postulates and Theorems

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  1. Proving Triangles Congruent jc-schools.net/PPT/geometrycongruence.ppt

  2. Angle-Side-Angle (ASA) Postulate 8-3: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

  3. Angle-Side-Angle (ASA) B E F A C D • A D • AB  DE • B E ABC DEF included side jc-schools.net/PPT/geometrycongruence.ppt

  4. Angle-Angle-Side (AAS) Theorem 8-1: If two angles and the nonincluded side of one triangle are congruent to two angles and the nonincluded side of another triangle, then the two triangles are congruent.

  5. Angle-Angle-Side (AAS) B E F A C D • A D • B E • BC  EF ABC DEF Non-included side jc-schools.net/PPT/geometrycongruence.ppt

  6. Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT jc-schools.net/PPT/geometrycongruence.ppt

  7. Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C F D NOT CONGRUENT jc-schools.net/PPT/geometrycongruence.ppt

  8. SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • SSA correspondence • AAA correspondence The Congruence Postulates jc-schools.net/PPT/geometrycongruence.ppt

  9. Name That Postulate (when possible) SAS ASA SSA SSS jc-schools.net/PPT/geometrycongruence.ppt

  10. Name That Postulate (when possible) AAA ASA SSA SAS jc-schools.net/PPT/geometrycongruence.ppt

  11. 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: jc-schools.net/PPT/geometrycongruence.ppt

  12. Another Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS: jc-schools.net/PPT/geometrycongruence.ppt

  13. Homework Work Packet: ASA and AAS

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