T H E O R M S TRIANGLES CONCEPT MAP Prove Triangles are Congruent Find Triangle Concurrencies Explore Triangle Inequalities How do we prove that 2 triangles are congruent? What are the characteristics of triangle concurrencies? How do we use inequalities in triangles? T H E O R M S Side-Side-Side (SSS) Congruence Postulate Side-Angle-Side (SAS) Congruence Postulate Hypotenuse-Leg (HL) Theorem Angle-Angle-Side (AAS) Theorem Angle-Side-Angle (ASA) Postulate If one side of a triangle is longer than the other side, then the angle opposite the longer side is larger than the angle opposite the shorter side. If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The Exterior Angle Inequality Theorem states that the measure of an exterior angle of a triangle is greater than the measure of either of the nonadjacent interior angles. The Hinge Theorem states that if 2 sides of 1 triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. The Converse is also a theorem. Centroid: Intersection of Medians Circumcenter: Intersection of Perpendicular Bisectors Incenter: Intersection of Angle Bisectors Orthocenter: Intersection of Altitudes