4-7 Medians, Altitudes, and Perpendicular Bisectors

Definitions

Median of a TriangleThe median of a triangle is a segment from a vertex to the midpoint of the opposite side.

How many medians in a triangle?

Altitude of a TriangleAn altitude of a triangle is the perpendicular segment from a vertex to the line that contains the opposite side.

How many altitudes in a triangle?

Altitude of Acute, Right and Obtuse TrianglesIn an acute triangle, the three altitudes are all inside the triangle.

In a right triangle, two are the legs of the right triangle and one is inside the triangle.

In an obtuse triangle, two are outside the triangle and one is inside the triangle.

Perpendicular Bisector of a Segment

A perpendicular bisector of a segment is a line (or ray or segment) that is perpendicular to the segment at its midpoint.