Lines of Symmetry in a Rectangle
In Geometry, a figure is said to be symmetrical when it is divided into two identical halves with the help of a line. These lines are called the lines of symmetry of a shape or figure.& A line of symmetry always cuts the shape into two equal and similar parts. There are different types of symmetries for a shape like linear symmetry, mirror symmetry, reflectional symmetry.
Let us read more about the lines of symmetry in a rectangle. We know that a rectangle is a special parallelogram whose opposite sides are equal and parallel. A rectangle has 2 lines of symmetry. Let us learn how to find the lines of symmetry in a rectangle.
| 1. | What are Lines of Symmetry in a Rectangle? |
| 2. | Rotational Symmetry of a Rectangle |
| 3. | FAQs on Lines of Symmetry in a Rectangle |
What are Lines of Symmetry in a Rectangle?
There are two lines of symmetry in a rectangle. When one line is drawn through the center along its length and the other is drawn along the width (breadth), we get the two lines of symmetry. By doing this, we get four equal and matching shapes. This can be tried out by taking a rectangular piece of paper. This is a simple technique of folding through which we can find out if a shape has a line of symmetry or not. If the folded part is placed exactly on the other one, then that folding line is called the line of symmetry. The figure shown below shows the lines of symmetry of a rectangle along its length and width. Each half is placed on the other when the rectangle is folded along the lines of symmetry. First, fold the paper horizontally to check the first line of symmetry and observe the size and shape of the equal halves. Then, fold it vertically to check the second line of symmetry to see the other identical halves.
It should be noted that the diagonals of a rectangle cannot be taken as lines of symmetry as they do not form equal matching shapes. Now, let us observe the following figure which shows why a rectangle does not produce two halves when folded across the diagonal. This is because, when we fold the rectangle along the diagonal line, we do not get two identical halves.
Rotational Symmetry of a Rectangle
If a figure or a flat shape is rotated along its axis and it still appears to be the same as before, we call it rotational symmetry. In other words, on partial rotation, if the shape remains the same as before, then there is rotational symmetry. A rectangle has a rotational symmetry when it is rotated by 180° and 360° on its axis. When a rectangle is rotated, it fits exactly on its boundary two times, once at 180° and once at 360°. In a rectangle the length is greater than its breadth, so we can say that there is no rotational symmetry at 90° and 270°.
Topics Related to Lines of Symmetry in Rectangle
Solved Examples
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Example 1: Check whether line 1 and line 2 marked in the figure are the lines of symmetry in the rectangle given below. Justify your answer.
Solution:
When the rectangle is folded along line 1, each of the parts formed by the line do not superimpose each other completely. The same thing happens when we fold it along line 2. So, we can say that line 1 and line 2 are not the lines of symmetry for this rectangle.
FAQs on Lines of Symmetry in a Rectangle
What are the Lines of Symmetry in a Rectangle?
The lines of symmetry in a rectangle are those lines that divide the rectangle into two identical halves. A rectangle has 2 lines of symmetry. One is drawn horizontally and the other is drawn vertically. It should be noted that the diagonals of a rectangle are not considered to be the lines of symmetry in a rectangle because they don't divide the rectangle into equal and identical halves.
What is a Line of Symmetry?
A line of symmetry can be defined as an imaginary line that is either drawn horizontally or vertically along the center of a shape to divide it into two equal halves.
How to find the Lines of Symmetry in a Shape?
When a shape is folded and if one half is exactly equal in size to the other half, then we say that the folded line is a line of symmetry. A shape can have more than one line of symmetry.
How many Lines of Symmetry does a Rectangle have?
A rectangle has two lines of symmetry. One along the side of length and another along the side of width.
How do I find the Lines of Symmetry in a Rectangle?
The lines of symmetry in a rectangle can be easily identified using a rectangular piece of paper. When we fold the rectangular piece of paper through its center horizontally or vertically we get two equal halves of the shape. Those folded lines are the lines of symmetry of a rectangle.
What is Rotational Symmetry?
A shape is said to have rotational symmetry if after some rotation by a certain angle it still remains in the same shape as it was ealier.
Does Rectangle have a Rotational Symmetry?
Yes, a rectangle has a rotational symmetry at 180° and 360°.