2. ORTHOCENTER (H) : The common intersection of the three lines containing the altitudes of a triangle.
3. CIRCUMCENTER (C) : The point in the plane equidistant from the three vertices of a triangle. Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, C is on the perpendicular bisector of each side of the triangle. It is the center of the CIRCUMCIRCLE.
4. INCENTER (I) : The point on the interior of a triangle that is equidistant from the three sides. Since a point interior to an angle is equidistant from the two sides of the angle lies on the angle bisector, then I must be on the angle bisector of each angle of the triangle. It is the center of the INCIRCLE (the inscribed circle) of the triangle.
5. MEDIAL triangle : The triangle connecting the three midpoints of the sides of a given triangle.
6. ORTHIC Triangle : The triangle connecting the feet of the altitudes of any acute triangle.
7. Let triangle ABC be any triangle. Then if P is any point in the plane, then the triangle formed by constructing perpendiculars to the sides of ABC locate three points R, S, and T that are the intersections. Triangle RST is the PEDAL Triangle for Pedal point P.
8. SCRIPT of NINE POINT CIRCLE