​Reflectional Symmetry

About Geometry Worksheet Assignment 3.8:     

 

Assignment 3.8 is an introduction to axes of symmetry and reflectional symmetry in polygons.

 

Prerequisite Skills:  Identify reflections (Assignment 3.7).

 

Definitions:  An axis of symmetry is a line intersecting the interior of a polygon that divides the polygon into two polygons that are reflections of each other.

                           A polygon with an axis of symmetry has reflectional symmetry.

 

Theorems:   In regular polygons, the number of axes of symmetry is equal to the number of sides in the polygon.

                           In regular polygons with an even number of sides, one-half of the axes of symmetry contain two vertices and one-half contain two midpoints.  

                           In regular polygons with an odd number of sides, each axis of symmetry contains a vertex and the midpoint of a side.