Reflection Symmetry

In our day to day lives, we witness numerous objects that have symmetry. An object or a figure is said to be symmetrical if it can be divided into two halves that are exactly equal. The line that divides the object or the figure into two equal halves or congruent halves is called the line of symmetry or the Mirror Line. In reflection symmetry, the first half is a reflection or mirror image of the second half.

Figures or objects can have more than one line of symmetry along which the figures or objects can be symmetrically divided. If a shape has one or more lines of symmetry, the shape is said to have reflection symmetry.

Important aspects of Reflection Symmetry:

1. A figure or shape or an object can have one or more than one line of symmetry.

2. The direction of the line of symmetry is not fixed.

3. Both the halves are congruent and mirror images of each other.

Example: Consider the shape of a heart held vertically. We can divide the heart into two equal halves along the central vertical line. This line is its line of symmetry.

The heart cannot be further folded to get the equal halves. Hence, the heart has only one line of reflection symmetry.

There are certain figures that possess more than one line of symmetry. E.g. – A rectangle:

As shown above, the rectangle can be divided into two equal halves either along the vertical line or along the horizontal line. Hence, a rectangle is said to have two axes of reflection symmetry.

One must note that not all shapes or figures have reflection symmetry. There are numerous shapes that cannot be divided into two congruent halves. Such shapes are called asymmetrical. 

Consider a scalene triangle: 

This triangle cannot be divided into equal halves and hence does not have reflection symmetry.

Reflection symmetry can also be illustrated by everyday objects like given below:

Explain how many lines of reflection symmetry do circle, square and an equilateral triangle have?

Since a circle can be divided into equal halves along its diameter and the fact that infinite diameters can be drawn for a circle, a circle is said to have infinite lines of symmetry. 

A square can be divided into equal halves by dividing horizontally, vertically or diagonally. Hence, a square is said to have 4 lines of symmetry.

Since the sides of an equilateral triangle are equal, it can be divided into equal halves by lines drawn from the midpoint of a side joining the opposite vertex. So, an equilateral triangle has 3 lines of symmetry. 

The isosceles triangle has two equal sides and therefore the line of symmetry or the reflection symmetry is two.

In all the above examples, there was only one line dividing the figure into two halves. There are many 3D objects where planes and not lines divide an object into two equal and congruent halves. Such planes are called planes of symmetry or planes of reflection. Consider a box or a container that you observe in a supermarket. 

Here, we can see that two planes divide the box into two equal halves. This object is said to have two planes of symmetry.

Reflection Symmetry is also called mirror symmetry or bilateral symmetry. In nature, reflection of mountains in rivers or lakes is a perfect example of reflection symmetry. Here, the line of symmetry is the ground line.

Problems on Reflection Symmetry:

1. Give four examples of reflection symmetrical objects from your home or at school?

Ans: Refrigerator, Washing Machines, Television Sets, Blackboards.

2. Which is the following two lines dividing the object is the line of reflection symmetry?

Ans: The line l2 is the reflection symmetrical line because it divides the shape or figure into two equal halves. The two halves that we get on division by line l2 are mirror images of each other.

3. Make the image above look symmetrical.

Ans: Consider that line l is the line of symmetry. Draw another ray starting at the base of the given line and it gives you two equal parts of the shape as shown below:

The mirror image will complete the figure as L is the line of symmetry.

4. List the number of lines of symmetry in each of the shape given in the image below:

Ans: (a) There are four lines of symmetry in this figure. (b) There are four lines of symmetry in this figure. (c) There are four lines of symmetry in this figure. (d) There are no lines of symmetry in this figure as the figure does not have any equal sides. (e) There are six lines of symmetry in this figure. (f) There are 6 lines of symmetry in this figure. (g) There are no lines of symmetry in this figure as its sides are unequal. (h) There are no lines of symmetry in this figure. (i) There are three lines of symmetry in this figure.

5. Can you draw a triangle having only one line of Symmetry?

Ans: Yes, we can draw an Isosceles triangle as it has only one line of symmetry. The sides of an isosceles triangle are the same or equal.

6. Which triangle has three lines of Symmetry?

Ans: An Equilateral triangle has three lines of symmetry. All three sides of an equilateral triangle are the same. 

7. How many lines of symmetry does a 5-pointed star have?

Ans: As we can see, the regular star can be divided into 2 halves in 5 ways. Hence, this is said to have 5 lines of reflection symmetry.

8. Divide the Alphabets from A to Z on the basis of their line of symmetry that is vertical, horizontal, no line of symmetry and make a list of Lines of symmetry.

Ans: The alphabets A, H, I, M, O, T, U, V, W, X and Y have a vertical line of symmetry. Whereas, the alphabets B, C, D, E, H, I, K, O and X have a horizontal line of symmetry. Some alphabets such as F, G, J, N, P, Q, R, S and Z have zero or no line of symmetry.

Reflection Symmetry in Nature

Nature has symmetry and rhythm. Even though nature is often associated with art, it should also be known that everything that is seen in nature is calculative and proportionate in design. The animals and even the human beings are in symmetry. Most of the species in nature are bilaterally symmetrical, and any given line of symmetry can divide a body into two equally symmetrical halves. Such animal organisms are called bilaterals. Each half consists of a pair of limbs, head and other organs. 

Reflection Symmetry in Art and Architecture

Most of the notable buildings are mirrored. Mathematics and architecture have always been interdependent on one another. There is no architecture with mathematics. The buildings are often designed to be symmetrical or often exact mirror images, in most of the architectural styles, reflection and symmetry were the core of it. 

Many churches that were built, were symmetrical both in elevation and in the plan. 

One such example is the VILLA ROTUNDA designed by Andrea Palladio. Other examples include; the Santa Maria Novella in France and Stonehenge as well.

Types of Symmetry

• Rotational symmetry

When an object is rotated around its axis at a certain angle, the object appears to be symmetrical even then, this kind of symmetry is defined as rotational or radial symmetry.

• Translation symmetry

When an object is moved forward or backwards in the same axis and the same plane and appears symmetrical, then this kind of symmetry is known to be translation symmetry.

• Reflection symmetry

The symmetry in which one half of an object is a mirror image of the other half is known as reflection symmetry. We see this kind of symmetry in nature, butterflies and the human body. 

• Glide symmetry

When an object is mirrored along a plane and then glided in a direction, the resulting symmetry is a combination of translation and reflective symmetry, it is known as glide symmetry.

Reflection

Reflection is a phenomenon in which the ray of light returns to its medium after touching an interface. The light, sound, and water waves are some of the examples that witness the phenomenon of reflection.

The Laws of Reflection

The following are the laws of reflection:

1. As per the laws of reflection, the reflected ray, the normal to the surface and the incident ray should all lie in the same plane.

2. The angle that the incident ray makes with the normal should be equal to the angle the reflected ray makes with the normal.

3. The incident ray and the reflected ray should lie on the opposite sides of the normal.

The Difference Between Reflection 

• In the phenomenon of reflection, the wave is bounced back into the same plane. Hence, there is no change in the medium. Whereas in refraction, the wave travels from one medium to another. Hence, there are two mediums involved in the phenomenon of refraction.

• The reflection usually occurs in mirrors. Whereas the refraction can be seen mostly in lenses.

• In reflection, the angle of incidence and the angle of reflection are the same. Whereas in refraction, the angle of incidence and the angle of refraction are not the same.

• In the phenomenon of reflection, the bending of light does not change the speed of the light. Whereas in refraction the speed of the wave changes due to the difference in medium.

• Reflection can be further classified into specular reflection and diffuse reflection. Whereas in refraction, there is only one type of refraction and isn't further classification.

Conclusion

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