The document discusses several shortcuts for proving triangle congruency: 1) Side-Side-Side (SSS): If two triangles have three corresponding pairs of sides that are congruent, then the triangles are congruent. 2) Side-Angle-Side (SAS): If two sides and the included angle in one triangle are congruent to two sides and included angle in another triangle, then the triangles are congruent. 3) Angle-Side-Angle (ASA): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent.