By, Alyssa Fountaine Sarah Dimick Spencer Mercure

Angle-Side-Angle (ASA) If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the tw0 triangles are congruent.

Side-Side-Side (SSS) If three sides of a triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Angle-Angle-Side (AAS) If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent.

Hypotenuse-Leg(HL) If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

CPCTC CPCTC: Congruent Parts of Congruent Triangles are Congruent Once you know that two triangles are congruent, you can make conclusions about corresponding segments and angles because of CPCTC.

Donkey Theorem and AAA “No Swearing in math class forwards or backwards.” Angle-Side-Side and Side-Side-Angle cannot be used to prove congruency because it cannot guarantee that one unique triangle will be drawn. Angle-Angle-Angle(AAA) cannot be used to prove congruency because two triangles can have the same angle but different side measures. They would be similar.

Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse: If two angles of a triangle are congruent, then the sides opposite the angles are congruent.

Corollary If a triangle is equilateral, then the triangle is equiangular. <X = <Y =<Z If a triangle is equiangular, then the triangle is equilateral. XY=YZ=ZX