Reflections & Line of Symmetry

Explore reflections and lines of symmetry in geometry. Grade 9 Alberta mathematics.

Lesson 7.4 of Similarity & Transformations in Grade 9 Math — Alberta curriculum lessons.

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What Is Symmetry?

Symmetry happens when a shape or object can be divided into two parts that are mirror images of each other.The Taj Mahal is a perfect example — its building and gardens were designed so that both sides look exactly the same.Symmetry gives shapes and designs a sense of balance, order, and beauty.

Line Symmetry

A line of symmetry (also called a mirror line or line of reflection) divides a figure into two identical halves.If you fold the shape along this line, both sides will match up perfectly — as if one side is reflected in a mirror.

Types of Lines of Symmetry

Lines of symmetry can be:

Lines of Symmetry in Regular Polygons

A regular polygon has sides and angles that are all equal.For these shapes, the number of lines of symmetry equals the number of sides.

Try This!

Draw regular polygons such as triangles, squares, pentagons, and hexagons.Use a ruler to find all possible lines of symmetry.You'll discover that: In every regular polygon, the number of lines of symmetry equals the number of its sides.

What Is a Reflection?

A reflection is a type of transformation that "flips" a shape over a line, creating a mirror image.The line you flip it over is called the line of reflection.In coordinate geometry, we usually reflect shapes across the x-axis or the y-axis.

Reflecting Across the x-Axis

When a point or shape is reflected across the x-axis:

For example:

Reflecting Across the y-Axis

When a point or shape is reflected across the y-axis:

For example:

Worked example: Example:

Does the Dashed Line Show Symmetry? Look at each shape and decide if the dashed line divides it into two matching halves.

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