Chapter 10 Section 3 Concurrent Lines

If the lines are Concurrent then they all intersect at the same point. The point of intersection is called the “point of concurrency”

4 different types of concurrent lines for a triangle I. I.Perpendicular bisectors II. II.Angle bisectors III. III.Altitudes IV. IV.Medians   Circumcenter   Incenter   Orthocenter   Centriod Concurrent Lines Name of Point of Concurrency

Theorem 10-1 The bisectors of the angles of a triangle intersect in a point that is equidistant from the three sides of the triangle The bisectors of the angles of a triangle intersect in a point that is equidistant from the three sides of the triangle Incenter

Theorem 10-2 The perpendicular bisectors of the sides of a triangle intersect in a point that is equidistant from the three vertices of the triangle The perpendicular bisectors of the sides of a triangle intersect in a point that is equidistant from the three vertices of the triangle Circumcenter

Theorem 10-3 The lines that contain the altitudes of a triangle intersect in a point. The lines that contain the altitudes of a triangle intersect in a point. Orthocenter

Theorem 10-4 The medians of a triangle intersect in a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. The medians of a triangle intersect in a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. Centroid