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Proving Triangles Congruent Free powerpoints at

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Two geometric figures with exactly the same size and shape. The Idea of a Congruence A C B DE F

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How much do you need to know... need to know about two triangles to prove that they are congruent?

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In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Corresponding Parts ABC DEF B A C E D F 1.AB DE 2.BC EF 3.AC DF 4. A D 5. B E 6. C F

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Do you need all six ? NO ! SSS SAS ASA AAS

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Side-Side-Side (SSS) 1. AB DE 2. BC EF 3. AC DF ABC DEF B A C E D F

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Side-Angle-Side (SAS) 1. AB DE 2. A D 3. AC DF ABC DEF B A C E D F included angle

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The angle between two sides Included Angle G I H

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

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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 include d 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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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) ASA 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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HW: Name That Postulate (when possible)

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HW: Name That Postulate

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Lets 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 AC FE

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HW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

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