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Proving Triangles Congruent Free powerpoints at http://www.worldofteaching.com The Idea of a Congruence Two geometric figures with exactly the same size and shape. F B A C E D How much do you need to know. . . . . . about two triangles to prove that they are congruent? 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. 1. AB DE 2. BC EF 3. AC DF 4. A D 5. B E 6. C F ABC DEF Do you need all six ? NO ! SSS SAS ASA AAS Side-Side-Side (SSS) 1. AB DE 2. BC EF 3. AC DF ABC DEF Side-Angle-Side (SAS) 1. AB DE 2. A D 3. AC DF ABC DEF included angle Included Angle The angle between two sides G I H Included Angle Name the included angle: E Y S YE and ES E ES and YS S YS and YE Y Angle-Side-Angle (ASA) 1. A D 2. AB DE ABC DEF 3. B E included side Included Side The side between two angles GI HI GH Included Side Name the included side: E Y S Y and E YE E and S ES S and Y SY Angle-Angle-Side (AAS) 1. A D 2. B E ABC DEF 3. BC EF Non-included side Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C D NOT CONGRUENT F The Congruence Postulates SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence Name That Postulate (when possible) SAS SSA ASA SSS Name That Postulate (when possible) AAA SAS ASA SSA Name That Postulate (when possible) Reflexive Property SAS Vertical Angles SAS Vertical Angles SAS Reflexive Property SSA HW: Name That Postulate (when possible) HW: Name That Postulate (when possible) Let’s Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AC FE For AAS: A F HW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:
