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.

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

What SSS Looks Like… A B C SP 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

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 – SideA – AngleS - Side B A CF D E  CAB  EFD because of SAS S: AB  FD A:  B   D S: BC  DE

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

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.

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 – AngleS – SideA - Angle B A CF D E  ACB  FED because of ASA

What ASA Looks Like…  FDG   JHG  MNL   PRQ D GJ 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

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