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

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

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

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

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

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.

The Congruence Postulates SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence

Name That Postulate (when possible) SAS ASA SSA SSS

Name That Postulate (when possible) AAA HL SSA SAS

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

Name That Postulate (when possible)

Name That Postulate (when possible)

Let’s Practice B  D AC  FE A  F Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B  D For SAS: AC  FE A  F For AAS: