Symmetry and Similarity Study Guide

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Updated on Oct 3, 2011

Introduction to Symmetry and Similarity

Symmetry, as wide or as narrow as you define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.

—Hermann Weyl (1885–1955)

In this lesson, you will see two different properties of figures—symmetry and similarity.

Shapes are said to be symmetrical if you can make a line through that shape, forming two halves that are mirror images of each other. Look at any figure and see if you can draw an imaginary line, such that if you folded the figure at this line, the figure would fall on top of itself. There can be none, one, or several lines of symmetry for a figure. Two types of symmetry are line symmetry and rotational symmetry.

A figure has line symmetry if it can be folded so that one half of the figure coincides with the other half.

Symmetry and Similarity

Congruent figures have the same size and shape. All corresponding parts, the sides and angles, have the same measure. They can be moved by a slide, flip, or turn. These movements are called transformations.

A reflection is where a figure is flipped over the line of symmetry, which divides a figure into two identical halves.

Symmetry and Similarity

Look at the letter A. If you split it in half with a vertical line, you end up with two identical halves.

Symmetry and Similarity

The letter A has line symmetry.

Now look at the letter Z. Can you draw a vertical or horizontal line to make two equal sides? No, so you know that the letter Z does not have line symmetry.

Symmetry and Similarity

A rotation is when something is turned completely around a central point. A figure has rotational symmetry if it looks exactly the same after it has been rotated 360 degrees.

2 Figures with Rotational Symmetry

A translation is a slide of a figure that slides every point of the figure the same distance in the same direction.


Similar Figures

Two figures are similar if they are the same shape but different sizes. The symbol for similarity is ~.

For four-sided figures, this means that corresponding angles are congruent, and corresponding sides are in proportion.

Symmetry and Similarity

If you are told that two figures are similar, then their corresponding sides are in proportion. If the scale factor is not apparent, set up a proportion. Remember, a proportion is an equation in which two ratios are equal. Proportional problems are solved using cross multiplication.

Find practice problems and solutions for these concepts at Symmetry and Similarity Practice Questions.

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