Understanding Reflection Symmetry

In daily life, the term ‘symmetry’ is often used. An object is considered symmetrical if it can be divided into two halves, and each half is the mirror image of the other. On the contrary, an object is deemed asymmetrical if the two halves do not mirror each other. Symmetrical objects are found everywhere, from nature to architecture to art. We are familiar with various types of symmetry, but this article will focus on line or reflection symmetry.

Reflection symmetry is a type of symmetry related to reflections. It's also referred to as line symmetry or mirror symmetry. This principle states that an object has reflection symmetry if at least one line can divide it into two halves, each being the mirror image of the other.

The line where a mirror can be positioned, such that one-half of the object mirrors the other, is known as the line of symmetry.
An object can have one or more lines of reflection symmetry.
The line of symmetry can be in any direction.

Illustrations of Reflection Symmetry

Regular polygons with N sides possess N lines of symmetry.

Triangle: 3 Lines of Symmetry

Square: 4 Lines of Symmetry

Pentagon: 5 Lines of Symmetry

A rectangle has both a vertical and a horizontal line of symmetry.

Rectangle: 2 Lines of Symmetry

However, it does not have symmetry across its diagonal.

Rectangle - not symmetrical across its diagonal

Does a Parallelogram Have Symmetry?

While a parallelogram might appear symmetrical at first glance, it does not have symmetry along any axis of reflection.

Reflection symmetry of Parallelogram

Reflection symmetry can also be observed in inkblot paper. By dropping a bit of ink and water on one side of the paper, folding it in half, and pressing it with your palm, you can create a symmetric pattern along the line of the fold. This fold line serves as the axis of reflection.

Reflection symmetry in inkblot paper

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Frequently Asked Questions

What is Reflection Symmetry?

Reflection symmetry is a type of symmetry which is with respect to reflections. It states that if there exists at least one line that divides a figure into two halves such that one half is the mirror image of the other half.