In view of the coronavirus pandemic, we are making LIVE CLASSES and VIDEO CLASSES completely FREE to prevent interruption in studies
Maths > Symmetry > Line of Symmetry
Symmetry

Line of Symmetry

Have you ever thought about how an artist makes a masterpiece through his artistry? Everything made by an artist is in the perfect line of symmetry. From sculptures to portraits an artist does wonders with his hands. But did you know that every creation of an artist is a balance of maths? Yes, the maths of symmetry harmonizes shapes and patterns. Let’s see how.

Suggested Videos

Play
Play
Play
Arrow
Arrow
ArrowArrow
Introduction to Linear Symmetry and Line of Symmetry
Introduction to Reflection
Construct a line segment symmetric to given line segment along a line of symmetry
Slider

 

Symmetry

From the most beautiful architecture of the world Taj Mahal to the modern skyscraping edifices, one thing common to these is the flawless symmetry of the structure. Symmetry is a very common word, but do you know how symmetry works, what effect it has or why do we need to put things in symmetry.

The answer seems simple, to give perfection to our creations, but is it that easy to bring creations under the line of symmetry? The answer becomes a yes when we know how the concept of symmetry works. Symmetry finds its origin in the Greek word which means “to measure together”. The concept of symmetry finds a great usage while studying geometry.

Mathematically, symmetry implies that shape which is an exact resemblance to its other part, when the shapes are divided into two or more equal parts.  Such shapes or figures or images are called symmetrical. The ones that do not resemble each other when divided into two parts are called asymmetric.

Browse more Topics Under Symmetry

Line of Symmetry

If in a shape or image, you draw a line down the centre and notice that the left side is a reflection of the right side then the image or shape is said to be as symmetry. For example, take your face. When we draw a line down our face exactly at the centre, then the left side of our face is symmetric to our right side of the face.

This defines symmetry. This line that divides a figure or shape or any image in identical halves then that figure is said to have a line symmetry. The line that divides a figure into identical halves is called the line of symmetry or the axis of symmetry. The line of symmetry is also called as mirror line because it produces two reflections of an image that coincide.

In the following figures notice the difference between symmetric and asymmetric figures. The figures in red colour when divided into two parts, are perfectly identical to their other half, showing them to be symmetrical while figures in black do not form identical halves there are asymmetrical.

Line of Symmetry

Types of Line of Symmetry

Lines of symmetry may be of two types:

Vertical Line of Symmetry

A vertical line of symmetry is that line which runs down an image thus dividing it into two identical halves. In other words, it is a straight standing line that divides an image or shape into two identical halves.

Line of Symmetry

Some English alphabets also show symmetry when divided into halves. A, H, M, O, W, U, Y, X etc are some alphabets that can be divided into equal halves by a vertical line of symmetry.

Horizontal Line of Symmetry

A horizontal line of symmetry is that line that runs across the image thus dividing into two identical halves. This line may also be called a sleeping straight line that parts an image or shape into identical halves.Line of Symmetry

English alphabets also are good examples of horizontal symmetry. Alphabets like C, E, H, K, O, X etc can be divided into equal halves by a horizontal line of symmetry.

Asymmetrical Shapes

There may be shapes and images that cannot be divided into identical halves, in such objects lines of symmetry cannot be drawn. These shapes or images are called asymmetrical shapes of images. A parallelogram is an asymmetrical figure as it has no line of symmetry.

Line of Symmetry

Some Points to Remember

There may be shapes which have more that one line of symmetry. These shapes have both vertical and horizontal lines of symmetry and are divided into more than two identical parts. For example rectangle, square and polygons like a pentagon or hexagon etc. A circle, however, has infinite lines of symmetry.

It is not necessary that symmetrical images have perfect shapes on all sides. The only condition for a shape to be symmetrical is that its one half is identical to the other.

For example, when a paper is blotted with different kinds of coloured inks and folded the image formed as a result of such blot is a symmetrical figure as well, though it has no definite shape and size. The point where the paper is folded is the line of symmetry for that image.

Solved Examples for You

Question 1: From the set of  following alphabets which set from the following are vertically symmetrical

  1. A, S, D, H, P
  2. T, M, N, J
  3. O, U, V, H, M
  4. G, W, Q, P

Answer : Option (C). Alphabets O, U, V, H, M are vertically symmetrical as these can be divided into identical halves with a line of symmetry running down their centre.

Question 2: What does symmetry mean in math?

Answer: Symmetry has its origin in the Greek word which translates “to measure together”. The concept of symmetry has great use in geometry. Symmetry in math means that shape which has an exact resemblance to the other parts when the shapes divide into two or more equal parts. Thus, we refer to these figures and shapes as symmetrical.

Question 3: What is line of symmetry?

Answer: A line which divides a figure or shape or any image in identical halves has line symmetry. Thus, the line which divides a figure into identical halves is referred to as the line of symmetry or the axis of symmetry. The line of symmetry is also referred to as mirror line.

Question 4: What are the types of line symmetry?

Answer: Lines of symmetry are of two types which are the vertical line of symmetry and horizontal line of symmetry. A vertical line of symmetry refers to one which runs down an image and thus divides it into two identical halves. Further, the horizontal line of symmetry is a line which runs across the image thus it divides it into two identical halves.

Question 5: What are asymmetrical shapes?

Answer: There are shapes and images that we cannot divide into identical halves, in such objects we cannot draw lines of symmetry. These shapes or images are referred to as asymmetrical shapes of images. For instance, a parallelogram is an asymmetrical figure because it does not have a line of symmetry.

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
tutor
tutor
Ashhar Firdausi
IIT Roorkee
Biology
tutor
tutor
Dr. Nazma Shaik
VTU
Chemistry
tutor
tutor
Gaurav Tiwari
APJAKTU
Physics
Get Started

Leave a Reply

avatar
  Subscribe  
Notify of

Stuck with a

Question Mark?

Have a doubt at 3 am? Our experts are available 24x7. Connect with a tutor instantly and get your concepts cleared in less than 3 steps.
toppr Code

chance to win a

study tour
to ISRO

Download the App

Watch lectures, practise questions and take tests on the go.

Get Question Papers of Last 10 Years

Which class are you in?
No thanks.