A rhombus is a quadrilateral where all the sides are of equal measure and the opposite sides are parallel. It is also defined as a parallelogram with adjacent sides of equal length. An imaginary line through which the rhombus is folded into two halves such that these halves are symmetrical in nature is known as a rhombus line of symmetry. Let's understand more about the rhombus lines of symmetry.
You are watching: How many lines of symmetry does a rhombus have?
|1.||Lines of Symmetry in Rhombus|
|2.||Lines of Rotational Symmetry in a Rhombus|
|3.||Lines of Symmetry in a Non Square Rhombus|
|4.||FAQs on Rhombus Lines of Symmetry|
Lines of Symmetry in Rhombus
There are 2 lines of symmetry in a rhombus. The imaginary axis or line along which the rhombus can be folded to obtain the two symmetrical halves is called the line of symmetry in rhombus. If the folded part exactly superimposes on the other half, with all the edges and corners coinciding, then the folded line represents a line of symmetry and that shape is symmetrical either along its length, width, or diagonals. The diagonals are the 2 lines of symmetry in a rhombus. This is because, when we fold the rhombus along the diagonal line, we get the same shape as two halves. Let's look into the diagram given below which shows the 2 lines of symmetry in a rhombus.
ABCD is a rhombus where the diagonals AC and BD are the two lines of symmetry shown using the dotted lines.
Lines of Rotational Symmetry in a Rhombus
A rhombus has rotational symmetry of order 2. Rotational symmetry is defined as a type of symmetry in which the image of a given shape looks exactly similar to the original shape or image in one full or 360° rotation. So, when a shape is turned about a complete rotation and the shape is identical to the origin, we see the rotational symmetry exists. We will completely rotate a rhombus by 360 degrees in different stages and check the images formed to check the order of the rotational symmetry as shown below.
From the above images of a rhombus, we observe that it fits onto itself twice in one full rotation of 360°. Therefore, we can conclude that the order of rotational symmetry in a rhombus is 2 and the angle of rotation is 180°.
Lines of Symmetry in a Non Square Rhombus
A square is a special type of rhombus with all its internal angles measuring 90° each. A non-square rhombus (also known as a rhombus) is different from a square with respect to its internal angles. Unlike a square, a non-square rhombus does not have all its internal angles equal to 90°. The number of lines of symmetry in a non-square rhombus is 2, whereas, a square has 4 lines of symmetry. The lines of symmetry in a square are drawn through its vertical axis, horizontal axis, and two diagonals whereas the lines of symmetry in a non-square rhombus are drawn through its diagonals. Let's look into the diagram below showing the lines of symmetry in a square and a non-square rhombus.
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Rhombus Lines of Symmetry Examples
Example 1: What are the angles at which a rhombus has rotational symmetry?
Rotational symmetry is defined as a type of symmetry in which the image of a given shape looks exactly similar to the original shape or image in one full or 360° rotation. So, when a shape is turned, and the shape is identical to the origin, rotational symmetry persists. Hence, a rhombus has a rotational symmetry at an angle of 180°.
Example 2: If a rhombus has one of its angles as an acute angle, how many lines of symmetry does this rhombus have?
It is given that one of the angles of the rhombus is an acute angle. Using this information we can conclude that the rhombus is not square-shaped. If all its angles were 90°, it would be a square that has 4 lines of symmetry. We know that a non-square rhombus has only 2 lines of symmetry through its diagonals. Therefore, the given rhombus has two lines of symmetry.
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FAQs on Rhombus Lines of Symmetry
What are the Lines of Symmetry in a Rhombus?
The diagonals of a rhombus represent the 2 lines of symmetry in a rhombus. They divide the rhombus into identical halves.
Does a Rhombus have any Lines of Symmetry?
Yes, a rhombus has two lines of symmetry through its diagonals.
Why Does a Rhombus have only 2 Lines of Symmetry?
A rhombus has only 2 lines of symmetry because when we fold the rhombus along its diagonal lines, we get the same shape as two halves which can superimpose on each other showing the symmetric nature.
How many Lines of Symmetry does a Non-Square Rhombus have?
A non-square rhombus, also known as a rhombus which is not a square has 2 lines of symmetry through its diagonal lines.
Does a Rhombus have four Lines of Symmetry?
Only a square rhombus has four lines of symmetry through its vertical axis, horizontal axis, and two diagonal lines, whereas, a rhombus that is not a square cannot have four lines of symmetry. It can only have two lines of symmetry.
What is the Smallest Angle of Rotational Symmetry for a Rhombus?
The smallest angle of rotational symmetry in a rhombus is 180°.
What Order of Rotational Symmetry does a Rhombus have?
The order of rotational symmetry is defined as the number of times that shape appears exactly the same in a complete 360-degree rotation. A rhombus has rotational symmetry of order 2 as it appears twice exactly the same in a complete rotation.
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How many Lines of Symmetry does a Rhombus have?
A rhombus has two lines of symmetry. The two diagonals of a rhombus are its lines of symmetry.