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FPT Sheet Chapter 4 POSTULATES If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. (SSS) 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. (SAS) If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. (ASA) THEOREMS The sum of the measures of the interior angles of a triangle is 180O. Corollary: The acute angles of a right triangle are complementary. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Triangle Congruence is: o Reflexive: ABC ABC o Symmetric: If ABC DEF , then DEF ABC o Transitive: If ABC DEF and DEF JKL, then ABC JKL If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. (RHL) If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. (AAS) 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. 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.