Section 6.6 Concurrence of Lines A number of lines are concurrent if they have exactly one point in common. m, n and p are concurrent. A m n p 12/4/2018 Section 6.6 Nack

Concurrent lines in Triangles Theorem 6.6.1: The three angle bisectors of the angles of a triangle are concurrent. The point at which the angle bisectors meet is the incenter of the triangle. It is the center of the inscribed circle of the triangle. 12/4/2018 Section 6.6 Nack

Perpendicular Bisectors Theorem 6.62: The three perpendicular bisectors of the sides of a triangle are concurrent. The point at which the perpendicular bisectors of the sides of a triangle meet is the circumcenter (center of the circumscribed circle) of the triangle. 12/4/2018 Section 6.6 Nack

Altitudes of a Triangle Theorem 6.63: The three altitudes of a triangle are concurrent. The point of concurrence for the three altitudes of a triangle is the orthocenter of the triangle. 12/4/2018 Section 6.6 Nack

Medians Theorem 6.6.4: The three medians of a triangle are concurrent at a point that is two-thirds the distance from any vertex to the midpoint of the opposite side. The point of concurrence for the three medians is the centroid of the triangle. Reminder: A median joins a vertex to the midpoint of the opposite side of the triangle. 12/4/2018 Section 6.6 Nack

Summary Summary of Chapter Six is on pages 329-330 12/4/2018 Section 6.6 Nack