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
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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.
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3. 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.
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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.
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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.
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6. Summary Summary of Chapter Six is on pages 329-330 12/4/2018
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