1. 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