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Proving Triangles Congruent

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Angle-Side- Angle (ASA) 1. A D 2. AB DE 3. B E ABC DEF B A C E D F included side

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The side between two angles Included Side GI HI GH

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

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Angle-Angle-Side (AAS) 1. A D 2. B E 3. BC EF ABC DEF B A C E D F Non-included side

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

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Warning: No AAA Postulate A C B D E F There is no such thing as an AAA postulate! 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 SAS ASA SSS SSA (when possible)

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Name That Postulate (when possible) HL SAS AAA SSA

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

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Name That Postulate (when possible)

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Name That Postulate

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

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