Lines of Symmetry in a Rectangle
In Geometry, symmetry means a line drawn on the center of a shape or a figure, divides the shape or figure exactly in to two equal halves, having the same shape and size. There are different types of symmetry for a shape. Some of them are linear symmetry, mirror symmetry, reflectional symmetry. Let's recall that a rectangle is a special parallelogram whose opposite sides are equal and parallel. A line of symmetry must cut the shape into two identical parts. A rectangle has 2 lines of symmetry. In this article, 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.||Solved Examples on Lines of Symmetry in a Rectangle|
|4.||Practice Questions on Lines of Symmetry in a Rectangle|
|5.||FAQs on Lines of Symmetry in a Rectangle|
What are Lines of Symmetry in a Rectangle?
A rectangle has its opposite sides to be equal and parallel. Whenever a figure in geometry is folded along a line of the symmetry the two halves formed look similar. In a rectangle, when a line of symmetry is drawn along its length and one along the breadth, we get two lines of symmetry. By doing this we exactly get four equal and matching shapes. The diagonals of a rectangle cannot be taken as a line of symmetry as they do not form equal matching shapes. This can be tried out by taking a rectangular shaped piece of paper and folding in half both horizontally and vertically to check if both the halves are equal in size and shape. The figure shown below shows the lines of symmetry of a rectangle along its length and breadth. Each half is superimposed on one another when the rectangle is folded along the lines of symmetry.
In a rectangle, we can also observe that the diagonals are not symmetrical. This is because, when we fold the rectangle along the diagonal line, we do not get the same shape as two halves. The figure given below shows why a rectangle does not produce two halves when folded across the diagonal.
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 as 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 for 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
Example 1: Check whether line 1 and line 2 marked in the figure are the lines of symmetries for the rectangle given below. Justify your answer.
When the rectangle is folded along line 1, each of the parts formed by the line do not superimpose each other completely. 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.
Example 2: What are the angles at which a rectangle has rotational symmetry?
A rectangle has rotational symmetry at 180° and 360°.
Example 3: Which of the following figures have rotational symmetry?
A circle has an infinite rotational symmetry, since it always fits in to the shape of a circle when it is rotated till 360°
A square has an order of rotational symmetry of 4, since it fits itself into the shape of a square every time it is rotated by 90°
A rectangle has an order of rotational symmetry of 2, since it fits itself into the shape twice. They are at 180° and 360°.
An equilateral triangle has an order of rotational symmetry of 3, since it fits itself thrice into the shape of triangle. The degrees of rotation are 0°, 120° and 240°
FAQs on Lines of Symmetry of a Rectangle
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 Do You Find Lines of Symmetry?
When a shape is folded and if the one half is exactly equal in size of the other half then we say that the folded line is a line of symmetry. A shape can also 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 for a Rectangle?
When we fold the rectangle through its center horizontally and 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 before.
Does Rectangle Have a Rotational Symmetry?
Yes, a rectangle has a rotational symmetry at 180° and 360°.