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**Proving Triangles Congruent**

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**Angle-Side-Angle (ASA)**

B E F A C D A D AB DE B E ABC DEF included side

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Included Side The side between two angles GI GH HI

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**Included Side Name the included angle: Y and E E and S S and Y**

YE ES SY

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**Angle-Angle-Side (AAS)**

B E F A C D A D B E BC EF ABC DEF Non-included side

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**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

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**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

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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.

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**The Congruence Postulates**

SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence

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Name That Postulate (when possible) SAS ASA SSA SSS

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Name That Postulate (when possible) AAA HL SSA SAS

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**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

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Name That Postulate (when possible)

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Name That Postulate (when possible)

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**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:

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Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 3.1 Congruent Triangles.

Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 3.1 Congruent Triangles.

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