Ways to Prove Triangles Congruent

Postulate 19, Side-Side-Side (SSS) Congruence Postulate - If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Postulate 20, Side-Angle-Side (SAS) Congruence Postulate - If two sides and the included angle of one triangle are congruent to two sides and the included angle in a second triangle, then the two triangles are congruent.

Postulate 21, Angle-Side-Angle (ASA) Congruence Postulate - If two angles and the included side of one triangle are congruent to two angles and the included side in a second triangle, then the two triangles are congruent.

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

4.6 Base Angles Theorem - If two sides of a triangle are congruent, then the angles opposite them are congruent.

Corollary - If a triangle is equilateral, then it is equiangular.

4.7 Converse of the Base Angles Theorem - If two angles of a triangle are congruent, then the sides opposite them are congruent.

Corollary - If a triangle is equiangular, then it is equilateral .

4.8 Hypotenuse-Leg (HL) Congruence Theorem - If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a secong triangle, then the two triangles are congruent.

4.2 Exterior Angles Theorem - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

4.3 Third Angles Theorem - If two angles of one triangle are congruent to two angles of another triangle then the third angles are also congruent.

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