Line of symmetry for regular polygon
Suppose, you went to visit the Taj Mahal with your friends.
While visiting Taj Mahal, you observed that both sides of the Taj Mahal are same .
Then, you asked your friend why the both sides of the Taj Mahal are equal.
Your friend told you that Taj Mahal is a symmetry.
He said that the line which is dividing the Taj Mahal into two half parts, is called the line of symmetry.
His friend explained that “if the object on one side of the axis is an exact replica or form of the object on the other side”. As
Then that object is considered to be in symmetry.
Then, you thought that if the line symmetry is in the Taj Mahal, then the other objects can also have line symmetry.
Similarly, we can see line of symmetry in other regular polygons too.
Let’s try to understand line of symmetry for regular polygon.
Suppose, we have equilateral triangle, square and regular pentagon.
We start with the equilateral triangle.
Here, we see this line
$AB$
is the line of symmetry which divides the triangle into two half parts.
Similarly, this line
$CD$
also divides the triangle into two half parts.
And, this line
$MN$
, also divides the triangle into two half parts.
So, basically there are
$3$
lines from
$3$
vertices to the opposite sides, which divides the triangle in two symmetrical parts.
Now, we have a square. As
In square, we have horizontal line of symmetry and also have vertical line of symmetry.
And, we also have two diagonals, which are line of symmetry in square.
Here we have
$4$
line of symmetry in case of square.
Now, we take a regular pentagon
$ABCDE$
.
We draw a line from point
$A$
to the midpoint of
$CD$
, which divides the pentagon into two half parts.
Similarly, we draw lines from point
$C$
and
$D$
respectively, which cuts the opposite sides at their midpoints.
Also, from point
$E$
to the mid point of
$BC$
, and from point
$B$
to the midpoint of
$ED$
.
So , we observe that there are total
$5$
line symmetry in a regular pentagon.
So, we conclude that “regular polygons have multiple lines of symmetry”.
Also, if the figure is a regular polygon than the number of “lines of symmetry” is equal to the number of sides in that polygon.
Revision
Regular polygons have multiple lines of symmetry.
If the figure is a regular polygon than the number of “lines of symmetry” is equal to the number of sides in that polygon.
The End