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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
How do you find it? Find the point of concurrency of the medians.


Special Properties:
1. The center of gravity for the triangular region.
2. The distance from the vertex to the centroid is twice the distance from the centroid to the side.
Location: Always inside the triangle.
Location:
Depends...
Obtuse - outside
Right - midpoint of the hypotenuse
Acute - inside
How do you find it?point of concurrency
of the perpendicular bisectors

Perpendicular bisector - perpendicular to a side and passing through the midpoint
Special Properties:
1. Equidistant to each vertex
2. You can make a circumscribe circle about the triangle or you can inscribe a triangle inside the circle.
How do you find it?
Point of concurrency of the angle bisectors
How do you find it?
Point of concurrency of the altitudes
Location:
Depends...
Acute - inside
Obtuse - outside
Right - on the right angle
Special
Properties:
None
Orthocenter
Altitude - perpendicular to a side and passing through the opposite vertex
Median: a line from the vertex to midpoint of opposite side
2. Center of the circle inscribed within the triangle (must construct the perpendicular segments to the sides to draw the circle)
Special Properties:
1. Equidistant from the vertices
Location:
Always inside the triangle.
Full transcript