Centroid - point where the three medians meet
Orthocenter - intersection point of the altitudes from the vertices of a triangle
Orthic Triangle - triangle created by connecting the orthocenter to the altitudes of the opposite sides
Orthocenter, Mid-segment Triangle
Circumcenter - point equidistant from the three vertices
Circumcircle - the circle that the triangle is inscribed in with the circumcenter as the center
Incenter - point of intersection of the angle bisectors of a triangle
Incircle - inscribed circle with the incenter as the radius
Equilateral Triangle given a side
Square given a side
Triangle Centers - circumcenter (C), centroid (G), orthocenter (H), and incenter (I)
Medial Triangle - triangle created by connecting the midpoints of the sides of a triangle
Golden
Ratio - point on a line segment that
makes the ratio 
Euler Line - line segment formed by the circumcenter (C), centroid (G), and orthocenter (H) of a triangle
Parabola - the set of points equidistant from a line, called the directrix, and a fixed point, called the focus
Pedal Triangle - triangle formed by connecting the intersections of the perpendiculars of the sides to an arbitrary point inside a triangle and the triangle sides