Pre-Algebra

5.8

Symmetry

Warm Up

Identify each as a translation, rotation, reflection, or none of these.

A. B.

reflection rotation

C.D.

none of the these translation

Learn to identify symmetry in figures.

line symmetry

line of symmetry

rotational symmetry

Vocabulary

Nature provides beautiful examples of symmetry, such as the wings of a butterfly or petals of a flower. Symmetric objects have parts that are congruent.

VOCAB: A figure has line symmetry if you can draw a line through it so the the two sides are mirror images of each other. The line is called line of symmetry.

If you fold a figure on the line of symmetry, the halves match exactly.

Helpful Hint

A.

Complete the figure. The dashed line is the line of symmetry.

Example: Drawing Figures With Line Symmetry

B.

Complete the figure. The dashed line is the line of symmetry.

Example: Drawing Figures With Line Symmetry Continued

A.

Complete the figure. The dashed line is the line of symmetry.

Try This

B.

Complete the figure. The dashed line is the line of symmetry.

Try This

VOCAB: A figure has rotational symmetry if you can rotate the figure around some point so that it coincides with itself. The point is the center of rotation, and the amount of rotation must be less than one full turn or 360°. To find the amount of degrees you can turn the figure so that it looks the same, divide 360 by the number of “folds”.

6-fold rotational symmetryThe figure coincides with itself every 60° (360/6)

8-fold rotational symmetryThe figure coincides with itself every 45° (360/8)

A. 2-fold

Complete the figure. The point is the center of rotation.

The figure coincides with itself every 180°

Example: Drawing Figures With Rotational Symmetry

B. 5-fold

Complete the figure. The point is the center of rotation.

The figure coincides with itself every 72°

Example: Drawing Figures With Rotational Symmetry Continued

A. 8-fold

Complete the figure. The point is the center of rotation.

The figure coincides with itself every 45°

Try This

B. 10-fold

The figure coincides with itself every 36°

Complete the figure. The point is the center of rotation.

Try This

Does the figure described have symmetry?

1. a regular hexagon

2. the letter F

3. the letter M

yes

no

yes

Lesson Quiz: Part 1

4. Complete the figure. The dashed line is the line of symmetry.

Lesson Quiz Part 2