How to Identify Shapes with Exactly 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 Understanding Two Lines of Symmetry in Geometry
1. What are two lines of symmetry?
Two lines of symmetry are two distinct lines that divide a shape into matching mirror-image halves. A shape with two lines of symmetry can be folded along either line so that both halves coincide exactly.
- Each line is called a line of symmetry or axis of symmetry.
- The shape must look identical on both sides of each line.
- Example: A rectangle (not a square) has exactly two lines of symmetry.
2. Which shapes have exactly two lines of symmetry?
Common shapes with exactly two lines of symmetry include a rectangle (not a square) and a rhombus (not a square).
- A rectangle has one vertical and one horizontal line of symmetry.
- A rhombus has two diagonal lines of symmetry.
- An ellipse (oval) also has two lines of symmetry.
3. How do you find the two lines of symmetry of a shape?
To find two lines of symmetry, draw lines that divide the shape into mirror-image halves. Follow these steps:
- Step 1: Fold the shape (mentally or physically) to see if both sides match.
- Step 2: Draw the line where the fold creates identical halves.
- Step 3: Check for another different line that also creates matching halves.
4. Does a rectangle have two lines of symmetry?
Yes, a rectangle has exactly two lines of symmetry: one vertical and one horizontal through its center. These lines:
- Pass through the midpoints of opposite sides.
- Divide the rectangle into two identical halves.
- Do not include the diagonals (unless it is a square).
5. Does a rhombus have two lines of symmetry?
Yes, a rhombus has exactly two lines of symmetry, which are its diagonals. These diagonals:
- Bisect each other at right angles.
- Divide the rhombus into identical mirror-image halves.
- Are symmetry lines only when the rhombus is not a general parallelogram.
6. What is the difference between two lines of symmetry and rotational symmetry?
Two lines of symmetry refer to reflection symmetry, while rotational symmetry refers to symmetry after turning a shape around a point.
- Line symmetry: Shape matches when folded along a line.
- Rotational symmetry: Shape matches after rotating by a certain angle.
- A rectangle has two lines of symmetry and rotational symmetry of order 2.
7. Can a triangle have two lines of symmetry?
No, a triangle cannot have exactly two lines of symmetry.
- An isosceles triangle has 1 line of symmetry.
- An equilateral triangle has 3 lines of symmetry.
- A scalene triangle has 0 lines of symmetry.
8. How many lines of symmetry does an ellipse have?
An ellipse has exactly two lines of symmetry: one along the major axis and one along the minor axis. These lines:
- Pass through the center of the ellipse.
- Divide it into two identical halves.
- Are perpendicular to each other.
9. What are examples of real-life objects with two lines of symmetry?
Real-life examples of objects with two lines of symmetry include rectangular doors, books, and certain logos.
- A rectangular notebook has one vertical and one horizontal symmetry line.
- An oval mirror has two symmetry axes.
- Some road signs shaped like rectangles show two reflection lines.
10. Why is understanding two lines of symmetry important in maths?
Understanding two lines of symmetry helps in identifying shape properties and solving geometry problems accurately. It is important because:
- It improves understanding of reflection symmetry.
- It helps classify quadrilaterals like rectangles and rhombuses.
- It supports learning about transformations and coordinate geometry.
