There are five ways to prove that triangles are congruent. They are:

SSS, SAS, ASA, AAS, HL

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 – Side S – Side S - SideB

A C F

D

E

ABC FDEbecause of SSS

S: AB FDS: BC DES: AC FE

What SSS Looks Like…

A

B

C

SP Q

R

E

D

F

ABC DEF

PRQ SRQ

S: AB EDS: BC EFS: AC FD

S: PR SRS: PQ SQS: 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 – Side A – Angle S - SideB

A C F

D

E

CAB EFD

because of SAS

S: AB FDA: B DS: BC DE

S: WT YZA: W ZS: WV ZX

L M

N

QP

WV

X

T

Y

Z

LMN QPN

YZX TWV

What SAS Looks Like…

S: MN PNA: LNM QNP

S: LN QN

What SAS Does NOT Look Like…

W VX

TY

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 DS: AB FDA: 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

What ASA Looks Like…

FDG JHG

MNL PRQ

D

G J

H

F

M N

PR

Q

L

A: D HS: DG HGA: DGF HGJ

A: N RS: MN PRA: 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

QL