Special Segments in Trianglesik,

Perpendicular Bisector

Line, segment, or ray that passes through the midpoint of a segment and is perpendicular to that segment.

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidstant from the endpoint of the segment.

Converse Perpendicular Bisector

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

Concurrent

Where three of more lines intersect at a common point

Point of Concurrency

The point where concurrent lines intersect.

Circumcenter

The point of concurrency of the perpendicular bisectors.

Circumcenter Theorem

The perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangles.

Angle bisector

Divides an angle into two congruent angles

Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

Converse of the Angle Bisector Theorem

If a point in the interior of an angle is equidistant from the sides of the angle, then is it on the bisector of the angle.

Incenter

The angle bisectors of a triangle are concurrent, and their point of concurrency is called ….

Incenter Theorem

The angle bisectors of a triangle intersect at a point called the incenter that is equidistant from the sides of triangle.

Median

A segment with endpoints being a vertex of a triangle and the midpoint of the opposite side.

Centroid

The point of concucrrency of the three medians of a triangle. Always inside triangle

Centroid Theorem

The medieans of a triangle intersect at a point called the centroid that is two thirds of the distance from each vertex to the midpoint of the opposite side.

Altitude

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

Orthocenter

The lines containing the altitudes of a triangle are concurrent, intersecting at point.

Incenter Diagram

Circumcenter Diagram

Centroid Diagram

Orthocenter Diagram