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

Explorations: