# 8.3: Reflection Symmetry

- Page ID
- 2164

Property of a shape with one or more lines of symmetry.

A **line of symmetry** is a line that passes through a figure such that it splits the figure into two **congruent** halves such that if one half were folded across the line of **symmetry** it would land directly on top of the other half.

**Reflection symmetry** is present when a figure has one or more lines of symmetry. These figures have reflection symmetry:

These figures __do not__ have reflection symmetry:

What if you had a six-pointed star, you drew a line down it, and then you folded it along that line? If the two sides of the star lined up, what would that mean about the line?

Example \(\PageIndex{1}\)

Find all lines of symmetry for the shape below.

**Solution**

Draw lines through the figure so that the lines perfectly cut the figure in half. This figure has eight lines of symmetry.

Example \(\PageIndex{2}\)

Find all lines of symmetry for the shape below.

**Solution**

You cannot draw lines through the figure so that the lines perfectly cut the figure in half, so this figure has no lines of symmetry.

Example \(\PageIndex{3}\)

Find all lines of symmetry for the shape below.

**Solution**

This figure has two lines of symmetry.

Example \(\PageIndex{4}\)

Does the figure below have reflection symmetry?

**Solution**

Yes, this figure has reflection symmetry.

Example \(\PageIndex{5}\)

Does the figure below have reflection symmetry?

**Solution**

Yes, this figure has reflection symmetry.

## Review

Determine whether each statement is true or false.

- All right triangles have
**line symmetry**. - All isosceles triangles have line symmetry.
- Every rectangle has line symmetry.
- Every rectangle has exactly two lines of symmetry.
- Every parallelogram has line symmetry.
- Every square has exactly two lines of symmetry.
- Every regular polygon has three lines of symmetry.
- Every sector of a circle has a line of symmetry.

Draw the following figures.

- A quadrilateral that has two pairs of congruent sides and exactly one line of symmetry.
- A figure with infinitely many lines of symmetry.

Find all lines of symmetry for the letters below.

Determine if the words below have reflection symmetry.

**OHIO****MOW****WOW****KICK****pod**

Trace each figure and then draw in all lines of symmetry.

Determine if the figures below have reflection symmetry. Identify all lines of symmetry.

## Review (Answers)

To see the Review answers, open this PDF file and look for section 12.1.

## Vocabulary

Term | Definition |
---|---|

Line of Symmetry |
A line of symmetry is a line that can be drawn to divide a figure into equal halves. |

Congruent |
Congruent figures are identical in size, shape and measure. |

Isosceles Triangle |
An isosceles triangle is a triangle in which exactly two sides are the same length. |

Line Symmetry |
A figure has line symmetry or reflection symmetry when it can be divided into equal halves that match. |

reflection symmetry |
A figure has reflection symmetry if it can be reflected across a line and look exactly the same as it did before the reflection. |

Symmetry |
A figure has symmetry if it can be transformed and still look the same. |

## Additional Resources

Interactive Element

Video: Reflection Symmetry Principles - Basic

Activities: Reflection Symmetry Discussion Questions

Study Aids: Symmetry and Tessellations Study Guide

Practice: Reflection Symmetry