What are the Lines of Symmetry in a Rhombus?
The term ‘line of symmetry in a rhombus’ refers to the imaginary axis or line that can be used to fold a rhombus into two symmetrical halves. A rhombus has two lines of symmetry. The two lines in a rhombus are its diagonals. The image illustrates a rhombus with two symmetry lines.
The rhombus ABCD has AC and BD as diagonals, which are its lines of symmetry. The two lines of symmetry are also represented using dashed lines.
[Note: A square has four lines of symmetry as all the internal angles of a square measure 90° each. These lines can be drawn through its horizontal axis, vertical axis and two diagonals.]
Now, let’s learn about the rotational symmetry of a rhombus.
What are the Lines of Rotational Symmetry of a Rhombus?
Rotational symmetry is a kind of symmetry in which the shape of a given figure looks exactly as the original figure when we rotate it by 360°. The rotational symmetry of a rhombus is of the order 2. To know how, check the examples provided in the image.
As seen in the examples, a rhombus can fit twice onto itself when rotated by 360°. Therefore, we can conclude that a rhombus has a rotational symmetry with order 2 and an angle of rotation of 180°.
Rapid Recall
Solved Examples
Example 1: A park is in the shape of a rhombus. Divide the park into multiple sections using each of its lines of symmetry. There are eight children in the park with an equal number of children in each section. How many children are in each section?
Solution:
The rhombus-shaped park has 2 lines of symmetry along its diagonals.
The lines of symmetry divide the park into four sections numbered 1, 2, 3 and 4 in the image.
Total number of children in the park = 8
Number of children in each section will be given by the total number of children divided by the number of sections, that is,
8 ÷ 4 = 2
Therefore there are 2 children in each section of the park.
Example 2: Christiana bought some square-shaped colored sheets to make origami to decorate her room. Can you calculate the number of folds she can make on each sheet of paper, so that every time she folds a sheet two of its parts are mirror images?
Solution:
As stated, Christiana bought square-shaped colored sheets to decorate her room.
We can say that the colored sheets are square rhombuses.
There are four lines of symmetry in a square rhombus as it has a vertical axis, a horizontal axis and the two diagonals.
Hence, Christiana can make four folds on each sheet of paper.
Example 3: Imagine a rhombus with one of its angles being an acute angle. Find the number of lines of symmetry of this rhombus?
Solution:
As mentioned, the given rhombus has an acute angle as one of its angles. From this information we can conclude that the given rhombus is not square-shaped as the angles are not right angles. We know, a non-square rhombus has only 2 lines of symmetry that are its diagonals.
Thus, the given rhombus has two lines of symmetry.
Rhombuses have two lines of symmetry. The two diagonals of rhombuses form the lines of symmetry.
Yes, a square rhombus has four lines of symmetry through its vertical axis, horizontal axis, and the two diagonals. Rhombuses that are not squares can only have two lines of symmetry.
The lines of symmetry help us to cut a shape exactly into two halves that are mirror images of each other.
A rhombus can be rotated symmetrically by 180° as it has rotational symmetry of the order 2.