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**Proving Triangles Congruent**

Free powerpoints at

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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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Congruent Triangles have six sets of corresponding parts! Three sets of corresponding sides Three sets of corresponding angles.

Congruent Triangles have six sets of corresponding parts! Three sets of corresponding sides Three sets of corresponding angles.

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