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Proving Triangles Congruent The Idea of a Congruence Two geometric figures with exactly the same size and shape. F B A C E D Corresponding Parts You will learn 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 How many of the 6 relationships do you need. . . . . .to prove that 2 triangles are congruent? Do you need ALL six ? NO! SSS SAS ASA AAS BUT ORDER MATTERS!!!! Side-Side-Side (SSS) S AB DE S BC EF S AC DF ABC DEF Side-Angle-Side (SAS) S AB DE A A D S AC DF ABC DEF included angle Included Angle The angle between two sides G I H Included Angle E Y S Name the included angle: YE and ES E ES and YS S YS and YE Y Angle-Side-Angle (ASA) A A D S AB DE ABC DEF A B E include d side Included Side The side between two angles GI HI GH Included Side E Y S Name the included side: Y and E YE E and S ES S and Y SY Angle-Angle-Side (AAS) A A D A B E ABC DEF S BC EF Non-included side Recap SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence BUT ORDER MATTERS!!!! Warning! No SSA Postulate No ASS Postulate because the triangles may or may not be congruent. NOT CONGRUENT Warning! No AAA Postulate No AAA Postulate because congruent angles do not always imply congruent sides! NOT CONGRUENT 3 3 8 8 3 8 Name That Postulate (when possible) SAS SSA ASA SSS Name That Postulate AAA SAS (when possible) ASA SSA Name That Postulate Reflexive Property SAS Vertical Angles SAS (when possible) Vertical Angles SAS Reflexive Property SSA HW: Name That Postulate (when possible) Reflexive Property SSS AS ASS AAA HW: Name That Postulate (when possible) Vertical Angles ASS ASA SAS Reflexive Property 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 OYO = On Your Own Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: N V For SAS: MK UT For AAS: M U Hypotenuse-Leg (HL) QRS and XYZ are right triangles H QS XZ L RS YZ QRS XYZ ONLY works for right triangles! (when possible) SAS Reflexive Property AAS Vertical Angles Reflexive Property HL ASS Another Big Idea: CPCTC • Stands for “Corresponding Parts of Congruent Triangles are Congruent” • Once you have already proved triangles congruent, you know that all corresponding sides and angles are congruent. 1. AB DE • Recall: If ABC DEF then 2. BC EF 3. AC DF 4. A D 5. B E 6. C F This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.