This document discusses two types of geometric symmetry: line symmetry and rotational symmetry. It defines line symmetry as when a figure can be divided into two mirror image parts by a line, called the line of symmetry. Rotational symmetry occurs when a figure looks the same after being rotated partway around a center point. Regular polygons have both types of symmetry: their number of lines of symmetry equals their number of sides, and their rotational symmetry angle is 360 degrees divided by the number of sides. The document provides examples and exercises to help understand and identify these symmetries.

1. Symmetry
A Look at How it Applies to Geometric Transformations

2. In this lesson, we will learn:
• What line symmetry is and how to identify it
• How to determine a line of symmetry
• About rotational symmetry and how to identify it
• How to determine a center and angle of rotational symmetry

3. Line Symmetry
• Also called reflection
symmetry
• When a figure or object can be
divided by a line into two
parts that are mirror images of
each other
• The line that divides the figure
or object is called the line of
symmetry
Image courtesy of Kokcharov via Wikimedia
Commons

4. More About Reflection Symmetry
Image from Public Domain

5. Line Reflection in Nature
Spider Crab, image from Public Domain

6. You Try—Does each figure have reflection
symmetry? If so, identify a line of reflection.

7. Check your answers.

8. A regular polygon has the same number of
lines of symmetry as it does sides.
Image courtesy of Greta Calleja

9. Rotational Symmetry
• When a figure or object can be
rotated about a point through
any angle that measures
between 0 and 360 degrees
and be its own image
• 0 and 360 aren’t included
because you are mapping the
pre-image onto itself
• The number of positions in
which the pre-image matches
the image is called the order
Triangle with 120 and 240 degree rotational
symmetry; of order 3; Image from Public
Domain

10. Regular Polygons and Rotational Symmetry
• All regular polygons have
rotational symmetry.
• The angle of rotational
symmetry can be found by
dividing 360 by the number of
sides
• Regular polygons have order
equal to the number of sides
This regular pentagon has five sides, so it
has rotational symmetry of 360/5, or 72
degrees. It has an order of 5.

11. You Try—Does each figure have rotational
symmetry? If so, state the angle of rotational
symmetry and the order.

12. Check your answers.
This has rotational symmetry
of 60 degrees. Order is 6.
This has rotational symmetry of
90 degrees. Order is 4.
No rotational symmetry
No rotational
symmetry