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Lines in a Triangle

Angle Bisectors
Divide each angle into two equal angles.

The intersection point of the angle bisectors is the center of the triangles inscribed circle.
 

Perpendicular Bisectors
A perpendicular bisector divides a side of a triangle into two equal lengths.

The perpendicular bisector runs at a right angle from the midpoint of the line segment.
The intersection point of the perpendicular bisectors is the center of the triangles circumscribed circle.

Median
A median goes from a vertex to the midpoint of the opposite side.

A median divides a triangle into two equal areas.
However, the perimeter can still differ.

The intersection of the medians is the centroid of the triangle.