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**Proving Triangles Congruent**

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**The Idea of a Congruence**

Two geometric figures with exactly the same size and shape. A C B D E F

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

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

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

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

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**Side-Angle-Side (SAS)**

B E F A C D AB DE A D AC DF ABC DEF included angle

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Included Angle The angle between two sides H G I

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**Included Angle Name the included angle: YE and ES ES and YS YS and YE**

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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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**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 ASA 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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**HW: Name That Postulate**

(when possible)

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**HW: 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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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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Ch 5. Proving Triangles Congruent (Sec 5.4 – Sec 5.6)

Ch 5. Proving Triangles Congruent (Sec 5.4 – Sec 5.6)

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