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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

Points of Concurrency in a Triangle
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.
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
Always inside the triangle
How do you find it?
Construct the altitudes.

A segment from the vertex perpendicular to the opposite side.
Special Properties:
Acute - inside
Obtuse - outside
Right - on the vertex of the right angle.
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