Relationships in Triangles

Perpendicular Bisector

In a triangle, a line, a segment, or a ray that passes through the midpoint of a side and is perpendicular to that side

Angle Bisector

In a triangle, a line, a segment, or a ray that divides an angle into two congruent angles.

Median

A segment joining a vertex to the midpoint of the opposite side

Altitude

A segment joining a vertex to the opposite side so that it is perpendicular to that side

Circumcenter

The perpendicular bisectors of the sides of a triangle intersect at a point

Incenter

The angle bisectors of the angles of a triangle intersect at a point

Centroid

The medians of the angles of a triangle intersect at a point

Orthocenter

The altitudes of the angles of a triangle intersect at a point

Circumcenter Theorem

The circumcenter is always equidistant from the vertices of the triangle.

Incenter Theorem

The incenter is always equidistant from the sides of the triangle.

Centroid Theorem

The centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side.

Midpoint

A point that divides a segment into two congruent segments

Perpendicular Slope

Negative Reciprocals