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Proving Triangles Congruent

Proving Triangles Congruent. Angle-Side- Angle (ASA). B. E. F. A. C. D.  A   D AB  DE  B   E. ABC   DEF. included side. Included Side. The side between two angles. GI. GH. HI. E. Y. S. Included Side. Name the included angle:  Y and  E

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Proving Triangles Congruent

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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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