centers of triangles

altitude of a triangle

A perpendicular segment from a vertex to the line containing the opposite side.

centroid of a triangle

The point of concurrency of the three medians of a triangle. Also called the center of gravity.

circumcenter of a triangle

The point of concurrency of the three perpendicular bisectors of a triangle.

circumscribed

A circle drawn on the outside of the triangle. Each vertex of the triangle lies on the circle.

equidistant

The same distance from two or more objects.

incenter of a triangle

The point of concurrency of the three angle bisectors of a triangle.

inscribed

A circle drawn inside a triangle.

median of a triangle

A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

orthocenter of a triangle

The point of concurrency of the three altitudes of a triangle.

If a point is on the perpendicular bisector of a segment…

… then it is equidistant from the endpoints of the segment.

If a point is equidistant from the endpoints of a segment…

… then it is on the perpendicular bisector of the segment.

If a point is on the bisector of an angle…

… then it is equidistant from the sides of the angle.

If a point in the interior of an angle is equidistant from the sides of the angle…

… then it is on the bisector of the angle.

The circumcenter of a triangle is…

…equidistant from the vertices of the triangle.

The incenter of a triangle is…

… equidistant from the sides of the triangle.

The centroid of the triangle is located…

…2/3 of the distance from each vertex to the midpoint of the opposite side.

centroid of a triangle

circumcenter of a triangle

incenter of a triangle

median of a triangle

perpendicular bisector of a triangle

angle bisector

altitude of a triangle

The incenter is eqadistant from the __ of the triangle?

sides

A circumcenter is equidistant from the _ of a triangle

vertices