Centroid - the intersection of the three medians of a triangle

Orthocenter - the intersection of the three altitudes of a triangle

Circumcenter - a point equidistant from the three vertices of a triangle

Incenter - a point in the interior of a triangle equidistant from all three sides of the triangle

Incircle - an inscribed circle within a triangle

Medial Triangle - a triangle with vertices of the three midpoints of a circumscribed triangle

Mid-Segment Triangle - a triangle DEF constructed by the vertices of the midpoints of triangle ABC

Orthic Triangle - a triangle DEF with vertices constructed by the intersection of the altitudes of vertices of triangle ABC and each respective opposite side

Pedal Triangle - a triangle DEF constructed by joining the intersections of perpendiculars from a given point O to the sides of a given triangle ABC

Center of Nine Point Circle - a circle centered around O the Orthocenter of triangle ABC

Nine Point Circle - a circle constructed by the nine points: 3 midpoints of each side of triangle ABC, 3 points of intersection of each side of triangle ABC and each respective altitude, 3 midpoints between each vertices and the Orthocenter along the vertice's corresponding altitude

Trisecting a Line Segment - a segment divided into three equal parts

Equilateral Triangle, give a side

Square, give a side

Isoceles Triangle, given base and altitude

Triangle Centers (H, G, C, I)

Triangle Centers with Euler Line - a line that passes through the Circumcenter, Orthocenter, and centroid of a given triangle

Locus of vertex of a Fixed Angle that subtends a fixed segment

Divide a Line Segment AB into two parts that form a golden ration

Pentagon, given a radius - 5 sided polygon with equal sides and angles

Pentagon, given a side - 5 sided polygon with equal sides and angles

Hexagon, given a side - 6 sided polygon with equal sides and angles

Octagon, given a side - 8 sided polygon with equal sides and angles