Reflection Symmetry: In our daily lives, we hear the word symmetry a lot. Symmetry can be found in nature and is also one of the most common themes in art, architecture, and design — in cultures all over the world and throughout human history. Leonardo da Vinci, as you may know, was fascinated by symmetry. As a result, he attempted to incorporate symmetry into many of his masterpieces, including The Last Supper, Vitruvian Man, and many others.

A symmetrical figure is one that is identical on both sides of a line. Aren’t you interested in learning more about symmetry? This article will go over reflection symmetry. Read on to find more.

What is Symmetry?

When a figure is folded into two halves such that both the halves are identical, we say that the figure is symmetrical. 
Look at the images given below.

In the above-given figures, the red coloured line divides each figure into two halves, and suppose we fold them along that line, and we will see that one half of each figure exactly coincides with the other half. A figure may have zero, one, two, three, or infinite lines of symmetry.

Now, there are two main types of symmetry. They are:
1. Rotational Symmetry
2. Reflection Symmetry

Rotational Symmetry

In our daily life, we come across many objects that rotate about a fixed point, such as the hands of a clock, the wheels of a vehicle, a ceiling fan or a windmill, etc. Some of these, as the hands of the clock and the blades of a fan, rotate only in one direction, while some objects rotate both clockwise and anti-clockwise.

A shape is said to have rotational symmetry when it looks the same even after a rotation. Rotation can be clockwise or anti-clockwise. When an object or a shape rotates, its size and shape do not change. Instead, it undergoes a turning movement about a specific point known as the centre of the rotation.

Let us understand it with the help of an example.

A paper windmill, though it looks symmetrical, it has no line of symmetry. But when you rotate it by a quarter of a turn, i.e., \(360^\circ \div 4 = 90^\circ \), it looks exactly like the original figure. So we say that it has rotational symmetry.

When an object is rotated, its shape and size do not change, and after a complete rotation of \(360^\circ \), it returns to its original position. Thus, a full turn is a rotation through an angle of \(360^\circ \), a half turn is a rotation through an angle of \(180^\circ \), and a quarter turn is of \(90^\circ \).

Some figures look the same when they are rotated about a certain point by a certain angle. For example, let us take a square and mark a dot at one of its corners to understand rotation.

Thus, the square, when rotated through angles of \(90^\circ,\;180^\circ,\;270^\circ\) and \(360^\circ\), looks exactly like the original figure.

Reflection Symmetry

In reflection symmetry, the line of symmetry divides a shape into two identical parts. Each part is identical to the other, or one part is the mirror image of the other.

Look at the images of symmetry provided to us by nature.

Aren’t they fascinating enough to motivate us to learn about reflection symmetry?

When an object is placed in front of the mirror, its image is formed in the mirror. The image in the mirror is as far behind the mirror as the object is in front of the mirror. So, a mirror behaves like a line of Symmetry. This phenomenon is called mirror reflection.

Thus, every line of symmetry is considered a mirror line. The line of symmetry can be in any direction, horizontal, vertical, slanting, etc. 

Meaning of Reflection Symmetry

The adjoining figure is said to have reflection symmetry about dotted line \(AB\). If the dotted line \(AB\) is considered to be a plane mirror, the image of the figure on the left side of the mirror line \(AB\) coincides with the figure on the right side of the mirror line \(AB\).

In the same way, the image of the figure on the right side of the mirror line coincides with the figure on the left side of the mirror line \(AB\). Thus, each of the following figures is said to have reflection symmetry about this mirror line.

Examples of Reflection Symmetry

The first basic thing to check is that one half should reflect the other half. Imagine folding a rectangle along each line of symmetry, and each of the halves matches up perfectly; this is considered symmetry. Thus, a shape must have at least one symmetry line to be considered a shape with reflection symmetry. Also, there is one most important property of reflection symmetry. One of them follows lateral inversion; that is left side appears to be the right side, as it happens when you look in a mirror. 

Remember when you lift your left hand up in front of the mirror, it appears like you have lifted your right hand.

The regular polygon of \(n\) sides has \(n\) lines of symmetry.

1. A triangle has \(3\) sides, so it has \(3\)-lines of symmetry.

2. A square has \(4\) sides, so it has \(4\)-lines of symmetry.

3. A pentagon has \(5\) sides, so it has \(5\)-lines of symmetry.

4. A hexagon has \(6\) sides, so it has \(6\)-lines of symmetry.

5. A line segment is symmetrical about its perpendicular bisector.

6. An angle (with equal arms) is symmetrical about its bisectors.

Let us have a look at some more images that shows reflection symmetry.

Solved Examples – Reflection Symmetry

Q.1. In the given figure, which one is the mirror line (line of symmetry) \(AB\) or \(CD\)?

Ans: Fold the figure about the dotted line \(AB\). The two parts of the figure (one is on the left side of \(AB\) and the other on the right side of \(AB\) coincide with each other. This implies that the figure given is symmetric about the mirror line \(AB\).

Now, fold the figure about the dotted line \(CD\). The two parts of the figure (one below \(CD\) and the other above \(CD\) do not coincide. This implies that the given figure is not symmetric about the line \(CD\). Hence, \(CD\) is not the mirror line for the given figure.

Q.2. Complete each of the following figures in such a way that the completed figure is symmetric about the given dotted line (line of symmetry).

Ans: We have to draw the complete figure so that the figure is symmetric about the given dotted line. Hence, the complete figure will be:

Q.3. If \(m\) is the mirror line and \(OA\) is an object in front of \(m\). Draw the reflected image of \(OA\).

Ans:

In the figure \(OA’\) is the reflected image of \(OA\).

Q.4. Find the reflection of a point \(A(x,y)\) in \(y\)-axis.

Ans: Let us take \(XOX’\) and \(YOY’\) as mutually perpendicular axes. The point \(A(x,y)\) and its image \(A'(-x,y)\) are marked as shown below.

Q.5. If m is the mirror line, then complete the shade by drawing the image of the object as shown in the below figure.

Ans: Mark \(B’\) the image of \(B\) such that
Perpendicular distance of \(B’\) from mirror line \(m=\) Perpendicular distance of \(B\) from mirror line \(m\).
Join \(B’\), and \(A\). Similarly mark other points of the image, i.e., \(C’, D’, E’, F’, G’\) and join \(B’C’, C’D’, D’E’, E’F’, F’G’\) and \(G’H\)

Thus the reflected shape \(AB’C’D’E’F’G’H\) is the image of \(ABCDEFGH\) in the mirror line \(m\).

Summary

In this article, we learned about symmetry and reflection symmetry. We learned the definition of reflection symmetry as well as rotational symmetry. We also learned that a regular polygon with \(n\) sides has \(n\) lines of symmetry. With the help of examples, we understood the concept of reflection symmetry.

Frequently Asked Questions (FAQ) – Reflection Symmetry

Q.1. Is symmetry found in nature?
Ans: Yes, our nature provides us with things full of symmetrical objects. For example, look at the starfish; most of the animals, leaves, flowers are grown to be perfectly symmetrical. Likewise, all snowflakes show a hexagonal symmetry around an axis that runs perpendicular to their face. 

Q.2. Explain reflection symmetry with an example.
Ans: In reflection symmetry, the line of symmetry divides a shape into two identical parts. Each part is similar to the other, or one part is the mirror image of the other. For example, imagine folding a rectangle along each line of symmetry, and each of the halves matches up perfectly; this is considered symmetry. Thus, a shape must have at least one symmetry line to be considered a shape with reflection symmetry.

Q.3. Does a square have reflection symmetry?
Ans: Yes, a square has a reflection symmetry with \(4\)-lines of reflection—two on the midpoints on the sides and two through the opposite vertices.

Q.4. How many lines of reflection symmetry do a rectangle have?
Ans: A rectangle has only \(2\)-lines of reflection symmetry.

Q.5. What is reflection symmetry in nature?
Ans: Reflection symmetry looks when a central mirror line can be drawn on it, and thus proving that both halves are symmetrical to each other or mirror reflection of each other. In our nature, there are a lot of symmetrical objects. For example, starfish, most animals, leaves, flowers, snowflakes, etc.

We hope this detailed article on reflection symmetry helped you in your studies. If you have any doubts or queries on it or any other topic, comment down below and we will be more than happy to help you.