Perpendicular bisector - a bisector of the segment that is perpendicular to the segment

Median - In a triangle, a segment that joins a vertex of the triangle and the midpoint of the opposite side

Altitude - a segment from the vertex of the triangle to the line containing the opposite side and perpendicular to the line containing that side

Angle bisector - In the figure below, the ray QS is the bisector of angle PQR if S is in the interior of the angle, and angle PQS is congruent to angle RQS

Theorem - any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment

Theorem - any point equidistant from the endpoints of a segment lies on the perpemdicular bisector of the segment

Theorem - any point on the bisector of an angle is equidistant from he sides of the angle

Theorem - any point on or in the interior of an angle and equidistant from the sides of an angle lies on the bisector of the angle

*Explorations with GSP