Proving Triangles Congruent Using SSS, SAS, and ASA

1. There are five ways to prove that triangles are congruent. They are: SSS, SAS, ASA, AAS, We are going to look at the first three today.

2. SSS Postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent . S Side S Side S - Side B A C F D E ABC FDE because of SSS S: AB FD S: BC DE S: AC FE

3. What SSS Looks Like A B C S P Q R E D F ABC DEF PRQ SRQ S: AB ED S: BC EF S: AC FD S: PR SR S: PQ SQ S: RQ RQ

4. SAS Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle , then the triangles are congruent. S Side A Angle S - Side B A C F D E CAB EFD because of SAS S: AB FD A: B D S: BC DE

5. S: WT YZ A: W Z S: WV ZX L M N Q P W V X T Y Z LMN QPN YZX TWV What SAS Looks Like S: MN PN A: LNM QNP S: LN QN

6. What SAS Does NOT Look Like W V X T Y Z The angle pair that is marked congruent MUST be in between the two congruent sides to use SAS! There is NOT enough information to determine whether these triangles are congruent .

7. A: B D S: AB FD A: A F ASA Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle , then the triangles are congruent. A Angle S Side A - Angle B A C F D E ACB FED because of ASA

8. What ASA Looks Like FDG JHG MNL PRQ D G J H F M N P R Q L A: D H S: DG HG A: DGF HGJ A: N R S: MN PR A: M P

9. What ASA Does NOT Look Like The pair of sides pair that are marked congruent MUST be in between the two congruent angles to use ASA! M N P R Q L