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Line Symmetry

This is a free geometry lesson on line symmetry for grades 3-4. It contains both teaching and varied exercises for the students.

These figures are symmetrical in relation to the dashed line.
The line is called a symmetry line. What does that mean?

Imagine that you folded the figure along the symmetry line.
Then both sides would exactly meet. Or, if you placed
a mirror along the symmetry line, you would see the
other half of the figure reflected in the mirror.

Many figures are not symmetrical at all.
You cannot draw a symmetry line in them.

1. Is the line drawn a symmetry line for the figure? You can cut out the images and fold them along the
    dashed line to check.

    a. b. c.









Some shapes you can fold in two different ways
so that the sides meet. The cross-shape
on the right has two different symmetry lines.

2. Draw as many different symmetry lines as you can into these shapes.






3. Write the capital letters in which you can draw a symmetry line. Draw the symmetry lines in them.




4. Draw a mirror image in the symmetry line to get a symmetrical figure.

a. b. c.

d. Continue the pattern. Then
    draw its mirror image.

e. Draw your own design
   and find its mirror image.

f. Draw your own design
   and find its mirror image.

5. Examining logos.  Look for logos on food products, cars, stores, magazines, and so on. Find at least
    three logos that have symmetry. Sketch them below. Answer the questions a. and b. for each logo.

    a. Does the logo employ a square, a rectangle, a triangle, a circle, or some other basic geometric
        figure in some way?

    b. Does it have any symmetry?

This lesson is taken from Maria Miller's book Math Mammoth Early Geometry, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

Math Mammoth Early Geometry

A self-teaching worktext for 1st - 3rd grade that covers basic shapes, right angle, symmetry, area, perimeter, and solids.

Download ($5.95). Also available as a printed copy.

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