Triangle Congruence Theorems

Side Angle Side

Side Side Side

Angle Side Angle

Angle Angle Side

Angle B is congruent to Angle D.

Angle BCA is congruent to Angle DCA

AC is congruent to AC

Triangle ABC is congruent to Triangle ADC

Hypotenuse Leg

Side Angle Side

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.

Side Side Side

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Angle Side Angle

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.

Angle Angle Side

If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.

Hypotenuse Leg

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.