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Points of Concurrency in a Triangle

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on 15 November 2013

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Transcript of Points of Concurrency in a Triangle

INCENTER
CENTROID
Circumcenter
Points of Concurrency in a Triangle
ORTHOCENTER
How do you find it?
Construct the angle bisectors.
angle bisector divides an angle in two equal parts
Special properties:
1. Equidistant from the sides of the triangle.
2. Center of an inscribed circle (measure the perpendicular distance from the incenter to the side)
Location: Always inside the triangle.
How do you find it?
Construct the perpendicular bisectors.
Perpendicular bisector: a line perpendicular to a line segment that passes through the midpoint.
Special Properties:
1. Equidistant from the vertices
2. Center of a circle circumscribed about the triangle.
Location:
Depends..,
Acute - inside
Obtuse - outside
Right - at the midpoint of the hypotenuse
How do you find it?
Point of concurrency of the three medians
Median: a segment connecting the midpoint of one side to the opposite vertex.
Special Properties:
1. Center of gravity for the triangular region
2. The dist. from vertex to centroid is twice the dist. from the centroid to the midpoint of the opposite side
Location:
Always inside the triangle
How do you find it?
Construct the altitudes.

Altitude:
A segment from the vertex perpendicular to the opposite side.
Special Properties:
None
Location:
Depends...
Acute - inside
Obtuse - outside
Right - on the vertex of the right angle.
Full transcript