Medians, Altitudes and Perpendicular Bisectors Section 4-7

Median Median of a triangle is a segment from a vertex to the midpoint of the opposite side. Medians intersect at a point called the centroid.

Centroid The distance from the cintroid to the midpoint of the side is half the distance from the centroid to the vertex.

Altitude Altitude of a triangle is the perpendicular segment from a vertex to the line that contains the opposite side. The altitudes of a triangle intersect at the Orthocenter.

Perpendicular Bisector Perpendicular Bisector of a segment is a line (or ray or segment) that is perpendicular to the segment at its midpoint. The perpendicular bisectors of a triangle intersect at the circumcenter

Angle Bisectors The angle bisectors of a triangle intersect at the incenter of a triangle.

Theorems If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment. If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment

Theorems Cont. If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle. If a point is equidistant from the sides of an angle, then the point lies on the bisector of an angle.