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ZingPath: Applying Transformations

Symmetry of a Figure

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Lesson Focus

Symmetry of a Figure


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A pattern is completed by forming congruent shapes using various symmetries of a given figure.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • After completing this Activity Object, learners will be able to:
  • Identify line symmetry of two-dimensional figures.
  • Identify point symmetry of two-dimensional figures.

Everything You'll Have Covered

There are two types of symmetry: line and point symmetry.

Line symmetry occurs when a line divides a geometric figure into two congruent portions. In other words, the part of the figure on one side of the line is a mirror reflection of the part on the other side of the line.


In each one of the above figures, the dotted line represents the line of symmetry splitting the figure so that both sides are congruent.

Non - Examples:

Neither of these figures has a line of symmetry, because the two sides of the figures are not congruent.

Point Symmetry exists when a figure is built around a single point called the center of the figure. For every point in the figure, there is another point found directly opposite it on the other side of the center. It looks the same when viewed from opposite directions - left to right, or turned upside-down.

A simple test to determine whether a figure has point symmetry is to turn it upside-down and see if it looks the same.A figure that has point symmetry is unchanged in appearance by a rotation.


There are many real-world examples of point symmetry. The snowflake and playing card shown below are examples of point symmetry.

A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps.

A regular tessellation means a tessellation made up of congruent regular polygons. Regular means that the sides of the polygon are all the same length. Congruent means that the polygons are all the same size and shape.

Only three regular polygons tessellate in plane geometry: triangles, squares, and hexagons. In this Activity Object, students complete a tessellation by choosing the correct symmetry of the figure.

Tutorial Details

Approximate Time 15 Minutes
Pre-requisite Concepts Students should know the definition of congruency.
Course Geometry
Type of Tutorial Skills Application
Key Vocabulary congruence, congruent, congruency of a figure