How do you prove two triangles are congruent?

Proving Triangle Congruence

To prove two triangles are congruent, you need to show all their corresponding sides and angles are equal. However, you don’t have to check all six parts! There are specific shortcut rules:

• SSS (Side-Side-Side): All three sides in one triangle are equal to the three sides in another.
• SAS (Side-Angle-Side): Two sides and the angle between them are equal.
• ASA (Angle-Side-Angle): Two angles and the side between them are equal.
• AAS (Angle-Angle-Side): Two angles and a non-included side are equal.
• HL (Hypotenuse-Leg, for right triangles): The hypotenuse and one leg are equal.

Short Example
If triangle ABC has AB=XY, BC=YZ, and CA=ZX, then by the SSS rule, triangles ABC and XYZ are congruent.

Takeaways

• Use one of the congruence rules (SSS, SAS, ASA, AAS, or HL) based on what info is given.
• You don’t need to check every angle and side-one correct rule is enough!