Products Of Mappings:

Products of mappings are denoted by AB: P ® P" stated as the B followed by A of P to P".

Theorem:

The product of two isometries is an isometry.

Theorem:

The product of a reflection in two parallel lines is a translation. All the
points are translated through twice the distance between the lines.

Theorem 12.7

The product of reflections in two intersecting lines is a rotation about
the point of intersection of the two lines. The angle of rotation is twice
the angle from the first line of reflection to the second line of
reflection.

Corollary:

A product of reflections in perpendicular line is a half turn about the
point of intersection of the lines.