4-7 Medians, Altitudes, and Perpendicular Bisectors Definitions

Median of a Triangle The 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 Triangle An 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 Triangles In 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.

Theorem 4-5 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. Theorem 4-6

Theorem 4-7 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 the angle. Theorem 4-8