# Chapter 5: Congruence Based on Triangles

• Chapter 5 Definitions, Postulates, and Theorems:

Altitude of a triangle is a line segment drawn from any vertex of the traingle perpendicular to and ending in the line that contains the opposite side.

Median of a triangle is a line segment that joins any vertex of the triangle to the midpoint of the opposite side.

Angle bisector of a triangle is a line segment that bisects any angle of the triangle and terminates in the side opposite that angle.

Isosceles Triangle Theorem: If two sides of a triangle are congruent, the angles opposite these sides are congruent.

If two angles of a triangle are congruent, the sides opposite these angles are congruent. *note - this is missing in the textbook!

Every equilateral triangle is equiangular.

The perpendicular bisector of a line segment is any line or subset of a line that is perpendicular to the line segment at its midpoint.

If two points are each equidistant from the endpoints of a line segment, then the points determine the perpendicular bisector of the line segment.

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

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

A point is on the perpendicular bisector of a line segment if and only if it is equidistant from the endpoints of the line segment.

The perpendicular bisectors of the sides of a triangle are concurrent  (cross at the same point.) The point where they meet is called the circumcenter.