triangles
angles in a triangle add to 180
constructing an equilateral triangle
perpendicular bisector of all sides passes through a common point (incomplete)
quadrilaterals
constructing a parallelogram with a given angle and with an area equal to a given triangle
circles
ellipses
getting the standard form equation from the geometric definition
the equivalence of the geometric definition and the conic section definition of an ellipse
the stretched cicle definition
the focus-directrix definition
the reflective property of an ellipse
a parallel projection of an ellipse is another ellipse (incomplete)
a cone can be created around any ellipse (incomplete)
parabola
the equivalence of the focus-directrix definition and the conic section definition of a parabola
getting the vertex form equation from the focus-directrix definition
getting the standard form equation from the vertex form
axis of symmetry of a parabola
getting the focus, directrix and vertex
hyperbola
the equivalence of the geometric definition and the conic section definition of a hyperbola (incomplete)
getting the standard form equation from the geometric definition
deriving the asymptote of a hyperbola
equation of the eccentricity (incomplete)
how a hanging chain forms a hyperbola (incomplete)
the area under between unit hyperbola, sinh(a) and cosh(a) is a/2 (incomplete)