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Symmetry

Definitions

line symmetry: A figure with line symmetry has two halves that are mirror images.

line of symmetry: The line along which a symmetrical figure is divided.

rotational symmetry: A figure with rotational symmetry can be turned around a central point less than 360° and be an exact image of itself.

center of rotation: The central point around which a figure is rotated.

Line Symmetry

Decide if each figure has line symmetry.

Figure 1: Can lines be drawn that divide the figure into mirror images? Yes.

Figure 2: No lines can be drawn to form mirror images.

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TEST TIME: Multiple Choice

How many lines of symmetry does the figure have?

You can draw 4 lines that divide the figure into mirror images.

Solution: The correct answer is c.

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Test-Taking Hint

Make notes in your test booklet to help you solve problems. For the problem above, drawing the lines of symmetry will help you see the mirror images. It will also help you count the number of lines of symmetry in the figure.

Rotational Symmetry

How many times will the figure show rotational symmetry within one full rotation?

Step 1: Draw lines from the center of the figure through identical places in the figure.

Step 2: Count the number of lines drawn.

The figure will show rotational symmetry five times within a full rotation.

Test-Taking Hint

Be careful to avoid careless answers on easy questions. Focus on each problem, and don’t be in a hurry.

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TEST TIME: Explain Your Answer

What kinds of symmetry does an equilateral triangle show? Explain.

Solution:

An equilateral triangle shows both line symmetry and rotational symmetry.

Because each side and each angle of an equilateral triangle are congruent, you can draw a line of symmetry running through each vertex and the center of the opposite side.

You can draw three lines from the center of the equilateral triangle through identical places in the figure. The triangle has rotational symmetry, and will show the symmetry three times within one rotation.

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