Question

Compare and contrast the terms median, altitude, and perpendicular bisector as they relate to a triangle.

Answer 1

A perpendicular bisector
is a segment that is perpendicular to a segment at it’s midpoint. ( 90 degrees )
Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.


A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.
Concurrency of Medians of a Triangle Theorem The medians of a triangle intersect at a point that is two-thirds of each segment.


The altitudes of a triangle is the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side.
• Concurrency of Altitudes Theorem The lines containing the altitudes of a triangle are concurrent.