How to Identify Shapes with Two 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: Definition & Examples
1. What is a line of symmetry?
A line of symmetry is an imaginary line that divides a shape or figure into two identical halves that are perfect mirror images of each other. If you were to fold the shape along this line, both halves would match up perfectly without any overlap.
2. What are some common examples of shapes that have exactly two lines of symmetry?
Several common shapes possess exactly two lines of symmetry. The most frequent examples taught in the CBSE syllabus are:
- A rectangle (that is not a square) has two lines of symmetry that pass through the midpoints of its opposite sides.
- A rhombus (that is not a square) has two lines of symmetry that run along its diagonals.
3. Which letters of the English alphabet have two lines of symmetry?
In the English alphabet, the capital letters that have exactly two lines of symmetry are H, I, and X. These letters can be divided into identical mirror-image halves both horizontally and vertically.
4. How many lines of symmetry does a rectangle have?
A rectangle has two lines of symmetry. One line runs horizontally through the midpoint of its shorter sides (width), and the other runs vertically through the midpoint of its longer sides (length). When folded along these lines, the parts of the rectangle overlap perfectly.
5. Why don't the diagonals of a rectangle act as lines of symmetry?
The diagonals of a rectangle do not act as lines of symmetry because if you fold a rectangular paper along one of its diagonals, the two halves do not overlap perfectly. The vertices of the folded part will not align with the vertices of the part underneath. This is a key difference from a square, where the diagonals are lines of symmetry because all its sides are equal.
6. Can a triangle have exactly two lines of symmetry?
No, a triangle cannot have exactly two lines of symmetry. A triangle can only have:
- One line of symmetry (an isosceles triangle).
- Three lines of symmetry (an equilateral triangle).
- No lines of symmetry (a scalene triangle).
7. How is line symmetry different from rotational symmetry for a shape like a rectangle?
Line symmetry and rotational symmetry are different geometric properties.
- Line Symmetry: This refers to folding a shape along a line to get two identical halves. A rectangle has two such lines.
- Rotational Symmetry: This refers to rotating a shape around a central point and having it look the same at certain angles. A rectangle has rotational symmetry of order 2, meaning it looks identical after a 180° and a 360° rotation.
8. What is the importance of understanding symmetry in Maths and the real world?
Understanding symmetry is important because it is a fundamental principle in geometry and design. In Maths, it helps in analysing shapes and understanding their properties. In the real world, symmetry is seen everywhere and is crucial in fields like:
- Art and Architecture: To create balance and aesthetically pleasing designs, such as in monuments and patterns.
- Nature: In the patterns of snowflakes, leaves, and the bodies of animals like butterflies.
- Engineering: To design stable, balanced, and functional structures and machines.
