Section 6.6 Concurrence of Lines

1. 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 Section 6.6 Nack

2. 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. Section 6.6 Nack

3. 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. Perpendicular Bisectors Section 6.6 Nack

4. 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. Section 6.6 Nack

5. 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. Section 6.6 Nack

6. Summary • Summary of Chapter Six is on pages 329-330 Section 6.6 Nack