An Overview of the Lines of Symmetry
The balanced and proportionate similarity between two halves of an object is termed as symmetry. In other words, one half is the mirror image of another half. It is necessary to understand the concept of line of symmetry. For example, when you fold the heart shape paper, the paper is folded from the centre to get the perfect symmetry of the heart. When you open the folded heart, you can find the line on the centre of the heart from where it is cut into two halves. This file which cuts the heart into two equal parts is known as the Line of Symmetry.
A figure which does not have any similarity between two halves is known as an asymmetrical figure. In an asymmetrical figure, none of the sides of the shape is equal.
You cannot fold the heart further to get the perfect symmetry. Hence, we can say that the heart shape has one and only one line of Symmetry. There are some figures wherein the lines of symmetry can be more than one. It is very important to understand the following points before studying the line of symmetry in detail.
If a figure or shape does not have a line of symmetry, it indicates that the shape or figure is asymmetrical.
Few shapes or figures have one line of symmetry, two lines of symmetry, or multiple lines of symmetry.
A circle can have an infinite number of lines of symmetry as it can be folded at any diameter to get the symmetrical halves. A square is said to have four lines of symmetry as its sides are the same, so the diagonal lines and vertical as well as horizontal lines divide a square. The equilateral triangle has three lines of symmetry whereas a scalene triangle does not have any line of symmetry as its all sides are different. An isosceles triangle has one line of symmetry as both of its sides are equal. A pentagon has five 5 lines of symmetry and a hexagon has six lines of symmetry.
Two Lines of Symmetry
Some figures can be divided into two equal parts with two lines. These shapes are said to have two lines of symmetry. The rectangle is an example of two lines of symmetry. A rectangle can be divided vertically, horizontally, or diagonally to get the two symmetrical parts. A rhombus also has two lines of symmetry. Two lines of symmetry can be a combination of vertical, diagonal, or horizontal lines. Letters such as H and X also have two lines of symmetry. An hourglass is also an example of two lines of symmetry.
A rectangle does not have a diagonal line of symmetry as opposed to a square as its sides are not the same. The rectangle can only have a vertical and horizontal line of symmetry.
In this figure, you can see that the rectangle is divided into equal parts vertically and horizontally. But if you draw a diagonal line from A to D, you can see that the sides will not match. You can try this with a piece of paper as well.
To Understand the Concept of Symmetry, let us Take up an Activity
Take a piece of A4 size of paper, and hold it vertically to get two equal halves. Then, fold it again vertically. Now, you can also draw a picture and cut the same. When you open the cutout picture, you will notice that the design you made also has two lines of symmetry.
One can also go to a supermarket and observe the lines of symmetry of different objects such as boxes, packages, containers, etc. You can also observe the fruits and vegetables around and try to find the line of symmetry of these various objects.
Problems on Line of Symmetry
1. Give four examples of symmetrical objects from your home or at school?
Answer: Inkpot, Notebook, Glass, and Backboard.
2. Identify the mirror line in the figure given below?
Answer: l2 as it divides the shape into two equal parts. The line of symmetry is the line which divides a shape or a figure in two equal parts.
3. Complete the diagram and make it look symmetrical. In the shape given below, L is the line of symmetry.
Answer: The line of symmetry divides the shape into two equal parts. Hence, the mirror image of this shape will complete the diagram.
4. In the figure given below, L is the line of symmetry. Draw the triangle to complete the diagram so that it looks symmetric.
Answer: Adding a mirror image will complete the figure given above and make it look symmetrical. The line of symmetry divides the shape into two equal halves; hence, the shape that one gets is given below:
5. List the number of symmetry lines in each of the shapes given below:
Answer:
(a) In figure A, there are four lines of symmetry.
(b) In Figure B, there are four lines of symmetry.
(c) In Figure C, there are four lines of symmetry.
(d) In figure D, there are no lines of symmetry.
(e) In figure E, there are 6 lines of symmetry.
(f) In figure F, there are 6 lines of symmetry.
(g) In figure G, there are no lines of Symmetry.
(h) In figure H, there are no lines of symmetry.
(i) In figure I, there are 3 lines of Symmetry
6. Can one draw a triangle having one line of symmetry?
Answer: Yes, an Isosceles triangle has one line of symmetry as both its sides are equal.
7. Can you draw a triangle with three lines of symmetry?
Answer: Yes, an equilateral triangle. The equilateral triangle has three lines of symmetry as all of its three sides are equal.
8. Make a list of lines of symmetry in Alphabets from A to Z. Divide them as per their lines of symmetry that is vertical, horizontal, no line of symmetry.
Answer:
Alphabets with vertical lines of symmetry: A, H, I, M, O, T, U, V, W, X, Y
Alphabets with horizontal lines of symmetry: B, C, D, E, H, I, K, O, X
Alphabets with no line of symmetry: F, G, J, N, P, Q, R, S, Z.
FAQs on Two Lines of Symmetry
1. What are lines of symmetry in a rectangle?
In a rectangle, there are two lines of symmetry, and these two lines of symmetry are constructed by drawing one of the lines through the centre along with its length and the other alongside its width (breadth). As a result, we have four equal and matching shapes. Using a rectangular piece of paper, you can experiment with this. This is a simple folding technique for determining whether or not a shape has a line of symmetry. When the rectangle is folded along the lines of symmetry, each half is placed on top of the other. First, check the first line of symmetry by folding the paper horizontally and observing the size and shape of the equal halves. Fold it vertically to see the other identical halves and check the second line of symmetry. It's worth noting that the diagonals of a rectangle aren't considered symmetry lines because they don't form equal matching shapes.
2. What is the rotational symmetry of a rectangle?
Rotational symmetry occurs when a figure or a flat form is rotated along its axis and yet appears to be the same as before. In other words, if the shape remains the same after partial rotation, there is rotational symmetry. When a rectangle is rotated 180° and 360° on its axis, it has rotational symmetry. When a rectangle is rotated 180° and 360°, it fits perfectly on its boundary both times. Because the length of a rectangle is bigger than its width, there is no rotational symmetry at 90° and 270°. Rectangle objects have the second-order of the rotation of symmetry. A rectangle is also a unique kind of quadrilateral, which has an equal number of opposite sides and all the angles of the rectangle present are 90 degrees.
3. What are the examples of two lines of symmetry?
Two lines of symmetry: The two lines of symmetry can be defined as when two lines can be used to divide a figure or structure into two equal sections. Two lines of symmetry exist in different shapes. Two lines of symmetry can be seen in the rectangle. The two symmetrical parts of a rectangle can be easily separated horizontally, vertically, or diagonally.
Here are some of the Examples of Two Lines of Symmetry
The Symmetry of a Rhombus: Mainly, there are two lines of symmetry alongside the diagonals of a rhombus.
The Symmetry of a Rectangle: the two lines of symmetry follow alongside the line segments which connect the mid-points of the opposite sides of a rectangle.
In English alphabets too, a few of the alphabets can be divided into two equal sections with the help of two lines of symmetry.
4. What are the figures with multiple lines of symmetry?
There are various figures in which there are more than two symmetry lines. Let’s have a look at the symmetry lines of some regular polygons.
Equilateral Triangle Symmetry Lines: Lines of symmetry in an equilateral triangle: Each angle of an equilateral triangle is 60 degrees, and all of its sides have the same length. It features three symmetry lines that run through its three medians.
Lines of Symmetry of a Square: A square is a quadrilateral with all of its sides equal and each of its angles being a right angle which is 90 degrees. Four symmetry lines, two diagonals, and two line segments connecting the mid-points of opposite sides make up a square.
Symmetry Lines of a Regular Pentagon: Each of the measures of the angle 108 is the same length on all sides of a regular pentagon. There are five symmetry lines in a normal pentagon.
Line Symmetry of a Regular Hexagon: Each of the measures of the angle 120 is equal on all sides of a regular hexagon. Three symmetry lines run diagonally and connect the mid-points of opposite sides of a regular hexagon.
5. What are the uses of figures with multiple lines of symmetry?
Symmetry can be seen in many places in our daily lives as it has much application which surrounds us. A few examples are stated below:
Multiple lines of symmetry can be seen in different works of art, various structures, and monuments. The use of symmetry can also be seen in nature as there are many things that have the application of symmetry within them. Leafs and butterflies are good examples of these.
Symmetry helps build beautiful buildings and monuments.
Multiple lines of symmetry are used to create patterns in painting.