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Understanding Triangle Congruence: Angle-Side-Angle (ASA) and Other Postulates

This guide provides a comprehensive overview of triangle congruence, focusing on the Angle-Side-Angle (ASA) postulate. It explains the conditions under which triangles are congruent, including Angle-Angle-Side (AAS) and the significance of the included side and angles. The guide emphasizes common misconceptions such as the non-existence of the SSA or AAA postulates. Through examples and practice problems, learn to identify congruence postulates and apply them effectively in various scenarios involving triangles.

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Understanding Triangle Congruence: Angle-Side-Angle (ASA) and Other Postulates

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  1. Proving Triangles Congruent

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

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

  4. E Y S Included Side Name the included angle: Y and E E and S S and Y YE ES SY

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

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

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

  8. Hypotenuse Leg (HL) • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

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

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

  11. Name That Postulate (when possible) AAA HL SSA SAS

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

  13. Name That Postulate (when possible)

  14. Name That Postulate (when possible)

  15. 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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