Transcript Document 7192002

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
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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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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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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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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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Summary
• Summary of Chapter Six is on pages 329-330
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