Triangle Properties: Medians, Altitudes, and Concurrency

Perpendicular Bisector

Line, segment, or ray that is perpendicular to the segment at its midpoint.

Angle Bisector

Ray or segment dividing an angle into two congruent angles.

Median of a Triangle

Segment whose endpoints are a vertex and the midpoint of the opposite side.

Altitude of a Triangle

The perpendicular segment from a vertex to the line containing the opposite side at 90 degrees.

Acute Triangle

All altitudes lie inside the triangle.

Right Triangle

Altitude is a side of the triangle.

Obtuse Triangle

Altitude lies outside the triangle.

Concurrent

Three or more lines intersecting at one point.

Point of Concurrency

The point where three or more lines intersect.

Circumcenter of Triangle

Point of concurrency of perpendicular bisectors of a triangle.

Incenter of Triangle

Point of concurrency of angle bisectors of a triangle.

Centroid of Triangle

The point of concurrency of the medians of a triangle.

Theorem 5-8

Medians of a triangle are concurrent at a point that is 2/3 the distance from each vertex to the midpoint of the opposite side.

Orthocenter of Triangle

The lines containing the altitudes of a triangle are concurrent at the _______.