THEOREMS:

The SAA or AAS Theorem - If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

The L-L Theorem( the Leg - Leg Theorem ) - If two legs of one right triangle are congruent to the corresponding legs of another right triangle, then the two triangles are congruent.

The L-AA Theorem ( The Leg - Acute Angle Theorem ) - If a leg and an acute angle of one right triangle are congruent to the corresponding leg and an acute angle of another, then the two triangles are congruent.

The H - AA Theorem ( The Hypotenuse - Acute Angle Theorem ) - If the hypotenuse and an acute angle of one right triangle are congruent to the corresponding hypotenuse and an acute angle of another, then the two triangles are congruent.

The H - L Theorem ( The Hypotenuse - Leg Theorem ) - If the hypotenuse and leg of one right triangle are congruent in the corresponding hypotenuse and leg  of another, then the two triangles are congruent.