Name: Real Life Examples on Symmetry
Uploaded: 2019-07-19
Duration: 1 min 32 s
Description: In this video, we will learn the concept of symmetry and various real-life examples of symmetry and the line of symmetry of different figures

Question

Some english alphabets have fascinating symmetrical structures. Which capital letters have only one line of symmetry(like E)? Which capital letters have rotational symmetry of order $2$ (like I)?

Fill the following table, thinking along such lines.

Alphabets	Line Symmetry	Number of lines symmetry	Rotational symmetry	Order of rotational symmetry
Z	No	$0$	Yes	$2$
S
H
O
E	Yes	$1$	No	-
N
C

Accepted Answer

We need to find the given alphabets' line symmetry with the number of lines and rotational symmetry with the order greater than $2$ (Order $1$ will not be counted).

Take the case of S.

A line of symmetry is a straight line dividing the figure into two parts such that, if these two parts are folded about this line, then they will superimpose each other.

For S, we cannot find any line that divides it into two equal parts.
So, there is no line of symmetry for the letter S.

If we rotate a figure about a fixed point by a certain angle and the figure looks exactly the same as before, the figure has rotational symmetry.

If we rotate S about its centre in $360 °$ , it looks the same.
Here the angle of symmetry is $360 °$ and the figure is turned for $1$ time before it comes to the original position.
So, the order of rotational symmetry is $1$ .

Take the case of H.

For H, we can find a horizontal line and a vertical line that divides it into two equal parts.
So, there are $2$ lines of symmetry for the letter H.

If we rotate H about its centre in $180 °$ , it looks the same.
Here the angle of symmetry is $180 °$ and the figure is turned for $2$ times before it comes to the original position.
So, the order of rotational symmetry is $2$ .

Take the case of O.

For O, we can find infinite number of lines that divide it into two equal parts.
So, there are infinite lines of symmetry for the letter O.

If we rotate O about its centre in any angle, it looks the same.
Here the angle of symmetry is infinity and the figure is turned for infinte times before it comes to the original position.
So, the order of rotational symmetry is infinity.

Take the case of N.

For N, we cannot find any line that divides it into two equal parts.
So, there is no line of symmetry for the letter N.

If we rotate N about its centre in $180 °$ , it looks the same.
Here the angle of symmetry is $180 °$ and the figure is turned for $2$ times before it comes to the original position.
So, the order of rotational symmetry is $2$ .

Take the case of C.

For C, we can find a vertical line that divides it into two equal parts.
So, there is $1$ line of symmetry for the letter C.

If we rotate C about its centre in $360 °$ , it looks the same.
Here the angle of symmetry is $360 °$ and the figure is turned for $1$ time before it comes to the original position.
So, the order of rotational symmetry is $1$ .

So, the final table looks like

Alphabets Line
Symmetry Number of lines
symmetry Rotational
symmetry Order of
rotational
symmetry

Z No $0$ Yes $2$

S No $0$ No -

H Yes $2$ Yes $2$

O Yes Infinity Yes Infinity

E Yes $1$ No -

N No $0$ Yes $2$

C Yes $1$ No -

Telangana Board Solutions for Chapter: Symmetry, Exercise 8: Exercise - 4

Telangana Board Mathematics Solutions for Exercise - Telangana Board Solutions for Chapter: Symmetry, Exercise 8: Exercise - 4

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