geometry

triangle related stuff

angles in a triangle add to 180

area of a triangle

constructing an equilateral triangle

pythagoras theorem

sides of 30 90 60

quadrilateral related stuff

area of a parallelogram

area of a trapezium

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

circle related stuff

Thales's theorem

parabola

getting the standard form equation of a parabola from the focus-directrix definition

axis of symmetry of a parabola

getting the focus, directrix and vertex

vertex equation of a parabola

the reflective property of a parabola

the equivalence of the focus-directrix definition and the conic section definition of a parabola

hyperbola

getting the standard form equation from the geometric definition

deriving the asymptote of a hyperbola

other shapes

lateral surface area of a right circular cone

lateral surface area of a right circular conical frustrum