Question

Compare and contrast the perpendicular bisectors, medians, and altitudes of a triangle. How are they alike? How are they different?

Answer 1

A perpendicular bisector is a line that intersects a given segment at a 90° angle, and passes through the given segment's midpoint.

A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

An altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base.