Regular Polygons and Symmetry

Polygons and Symmetry

​There are two kinds of symmetry:

1) Line Symmetry

2) Rotational Symmetry


with two kinds of polygons:

1) Regular

2) "Non" regular/irregular

Regular Polygon

• has all sides equal/congruent

  (same length)

Lines of Symmetry

• The line of symmetry can be defined as the imaginary line that passes through the center of the shape or object.

• It divides the figure into identical halves.

Regular Polygons

Number of Sides = Number of lines of symmetry

Equilateral Triangle

• Three equal sides

• Three lines of symmetry

Square

• Four equal sides

• Four lines of symmetry

Regular Pentagon

• Five equal sides

• Five lines of symmetry

Regular Hexagon

• Six equal sides

• Six lines of symmetry

and so on ...

Multiple Choice

A regular dodecagon has twelve sides. How many lines of symmetry does it have?

• 2

• 4

• 6

• 12

• 24

​What about figures that are not regular?

​

​Notice these polygons do NOT have all sides equal.

Multiple Choice

How many lines of symmetry does this trapezoid have?

• 0
• 1
• 2
• 4

Multiple Choice

How many lines of symmetry does this parallelogram have?

• 0

• 1

• 2

• 4

Rotational Symmetry

If a figure is rotated around a center point and it still appears exactly as it did before the rotation, it is said to have rotational symmetry.

In the images to the right, these "non" regular polygons have either no rotational symmetry or 180 degrees of rotational symmetry.

For Regular Polygons, it's easier ...

Equilateral Triangle

Multiple Choice

What are the angles of rotational symmetry for a square?

• Multiples of 30°

• Multiples of 45°

• Multiples of 90°

• Multiples of 180°

Multiple Choice

Identify the smallest angle of rotational symmetry that maps the regular pentagon onto itself.

• 72°
• 180°
• 144°
• 45°