The Pythagorean Theorem: If is a right triangle with the right angle at , then

(C.117) |

In a given circle, equal arcs subtend equal chords.

A regular hexagon inscribed in a circle has each of its sides equal to the radius of the circle. The radii joining the vertices of this hexagon to the center of the circle decompose the hexagon into six equilateral triangles.

It is assumed that you are familiar with the process of representing points in the plane by pairs of numbers. If and are points with , then the slope of the segment joining to is defined to be

(C.118) |

If we say that has *undefined slope*, or that
is a *vertical* segment.
If slope is zero
we say that is a *horizontal* segment.

Let and
be two distinct points in the plane.
If , then the line passing through and is
defined to be the set
of all points of the form , where can be an arbitrary real
number. If , then the *line joining* *to*
is defined to be
the set consisting of together with all points
such that slope() = slope(). Thus if then
is on the line joining
to if and only if

If then (C.120) is called an

(C.121) |

Two lines are *parallel*, (i.e. they do not
intersect or they are identical,) if and only if they both have the same
slope or they both
have undefined slopes.