geometry

triangles

angles in a triangle add to 180

area of a triangle

constructing an equilateral triangle

pythagoras theorem

sides of 30 90 60

quadrilaterals

area of a parallelogram

area of a trapezium

constructing a parallelogram with a given angle and with an area equal to a given triangle

circles

the perpendicular bisector of a chord is the diametre

Thales's theorem

inscribed angle theorem

every triangle can be circumscribed by a circle

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

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

the reflective property of a parabola

hyperbola

getting the standard form equation from the geometric definition

deriving the asymptote of a hyperbola

equation of the directrix

other shapes

lateral surface area of a right circular cone

lateral surface area of a right circular conical frustrum