Symmetry Class 6 Maths NCERT Chapter 13

Key Features of NCERT Material for Class 6 Maths Chapter 13 – Symmetry  

In previous chapter 12, we learned about ratios, it’s applications and proportions, In chapter 13 of Class 6 Maths NCERT book: Symmetry, we will study symmetry, it’s applications and types of symmetry. We will also look at symmetry in different shapes.

Quick revision notes

In our day by day life symmetry is a typical term. At the point when we see a figure with uniformly adjusted extents, at that point we state that it is symmetrical. 

If we can fold a picture into equal parts with the end goal that the left and right parts coordinate precisely, at that point the image is said to have line symmetry. We can see that the two parts are perfect representations of one another. If we place a mirror on the crease, at that point, the picture of one side of the image will fall precisely on the opposite side of the image. The line of the fold is known as the line of symmetry. It separates the figure into two same parts. 

Symmetry  and Asymmetric

Making Symmetric Figures: Ink-Blot Devils 

We can list a couple of articles from our surrounding of symmetry for these symmetric items. Additionally, we can recognize the lines of symmetry. Symmetry has various applications in our everyday life. For instance, in art, architecture, engineering, technology, plan relations, Rangoli, and so forth.

Line symmetry

A figure has line symmetry if a line is drawn isolating the figure into two equal parts. The line is known as a line of symmetry. For instance: The dotted lines in the below figure shows line symmetry.

Line symmetry

Bilateral symmetry 

On the off chance that a figure is isolated along with two parts by just one line and these parts cover each other totally, at that point the figure is said to have bilateral symmetry. 

For instance: A butterfly shows two-sided symmetry.

Bilateral symmetry 

Figures with Two Lines of Symmetry 

In the event that we take a rectangular sheet and fold it lengthwise or breadthwise, we locate that one half fits precisely over the other half. We state that a rectangle has two lines of symmetry. 

Note: An isosceles triangle has just one line of symmetry. 

In a scalene triangle, there is no line of symmetry. 

Figures with Multiple Lines of Symmetry (more than two)

An Equilateral Triangle has three lines of symmetry while a circle has innumerable lines of symmetry. 

Multiple Lines of Symmetry

Lines of Symmetry in Polygons 

Polygons are closed figures made of at least three line segments. Triangle is a polygon with the least number of the line segments. Some different instances of polygons are Square, Rectangle, Pentagon, Hexagon, Septagon and so on. Polygons might be ordinary and sporadic. 

Normal polygons are symmetrical and partitioned by more than one line of symmetry to shape alike parts. A square shape is partitioned into symmetrical parts with the assistance of two lines. A symmetrical triangle is separated into alike parts with the assistance of three lines of symmetry going through its inside. In like manner, four lines isolate a square into completely symmetrical parts. 

Reflection and Symmetry 

The line symmetry firmly identifies with mirror reflection. In mirror reflection, we need to consider the left-right changes in direction. 

Reflection and Symmetry 

Reflection Symmetry 

Reflection symmetry is fundamentally the same as line symmetry aside from the adjustment in direction.  For instance, when you see yourself in the mirror, your right-hand turn into the left hand in the mirror.

So when we see a picture of an item in the mirror, at that point the article is symmetrical with its mirror image. This view is like a collapsed paper. At the point when a paper is collapsed precisely in the centre, the line of the overlap is the line of symmetry. This line of the fold resembles the mirror line. The picture framed in the mirror is a reflection of the article in the line of symmetry.

Point Symmetry 

Point symmetry exists when we draw a figure around a single point. It is for figures having a point through which the symmetry can be set up. This point is the centre of symmetry. For instance, the hourglass shows point symmetry

Point Symmetry 

Rotational Symmetry  

Rotational Symmetry  

 It isn’t vital that an item should consistently have a line of symmetry to demonstrate its symmetrical trait. There might be a few items which show symmetry even when the line of symmetry is absent. Such symmetrical items show rotational symmetry. 

Also called radial symmetry, rotational symmetry is that trademark wherein the item looks same even after rotating it. At the point when an article turns around a fixed axis if its appearance of size and shape doesn’t change, at that point the item should be rotationally symmetrical. The reusing symbol is likewise a case of rotational symmetry.


A kaleidoscope utilizes mirrors to deliver pictures that have several lines of symmetry. Generally, it has two mirror strips framing a V-shape. The point between the mirrors decides the number of lines of symmetry. 

The following figure shows the example shaped by a kaleidoscope.


Question: What do you mean by symmetrical shape? 

Answer: Generally, symmetry is when something is the equivalent on the two sides. Also, an article has symmetry if a center line separating it (a mirror line) can be drawn on it. Besides, it shows that the two sides of the shape are equivalent. In basic words, symmetrical shapes allude to those shapes which when cut into half look simply like the other half.

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