In order to take the guess work out of proving if triangles are congruent there are five methods used to prove if the triangles are congruent

Proving Triangles Congruent/ Side Side Side

HL

Angle Side Angle

Hypotenuse Leg

Angle Angle Side

AAS

ASA

SSS

SAS

SSS The three sides of one triangle are congruent to the three sides of another triangle

Side Angle Side

SAS Side Angle Side The two sides plus the included angle of one triangle are congruent to the two sides plus the included angle of another triangle

ASA Two angles and the included side of one triangle is congruent to two angles and the included side of another triangle. The side between the two angles being used is the included side.

AAS Two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle. Either side that is not between the two angles being used is can be a non-included side

HL Hypotenuse leg The hypotenuse and leg of one right triangle is congruent to the hypotenuse and leg of another triangle

Proving Triangles Congruent

Click on the picture for the full size "Proving Triangles Congruent" Infographic

Proving Triangles Congruent

Proving Triangles Congruent/Infographic

CPCTC is an acronym for correspondingparts of congruent triangles are congruent. This theorem states that once two triangles are proven to be congruent, then the three pairs of sides and angles that correspond must be congruent. The following video shows how to use CPCTC