Theorems
Midsegment Theorem
The segment connecting the midpoints of two sides of the triangle, is parallel to the third side and is half as long as that side.
A segment that connects the midpoints of two sides of the triangle
Midsegment
The point of concurrency of the medians of a triangle
Centroid
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the sides of the angle
Median
A segment from a vertex to the midpoint of the opposite side.
The point of concurrency of the angle bisectors of a triangle.
Incenter
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
The perpendicular segment from the vertex to the opposite side of the triangle
The point of concurrency of the lines containing the altitudes of the triangle.
Orthocenter