Polygons are closed figures made up of lines
and points. The vertices of the polygon are the
points, and the sides of the polygons are lines
connecting those points. An n-gon is a short hand way
of denoting a polygon of n sides and n vertices.
A quadrilateral is a four-sided polygon. Certain
quadrilaterals have special names: rectangle, square,
parallelogram, rhombus, trapezoid, and kite depending
on their properties. One problem in mathematics is
what is the least number of properties that must be
defined to charactierize an object.
For example, a square can be defined as
quadrilateral of 4 equal sides and one right angle.
However, a square can also be defined as a
quadrilateral with two adjacent sides equal, one right
angle, and two opposite sides parallel OR as a
quadrilateral with diagonals which are equal and
perpendicular to each other. Which properties are
preferred as a definition of a square?
The issue is not so much which properties are
preferred, but are they equivalent? In other words,
given one definition, can the others be proven from
that starting point?
