Lines of Symmetry in a Parallelogram
A parallelogram is a type of quadrilateral where the opposite sides are parallel and equal. The imaginary line so formed along which you can fold a figure to obtain the symmetrical halves is referred to as the line of symmetry. Thus, the lines of symmetry of a parallelogram refer to the lines cutting the parallelogram into two identical parts. Also, the lines of symmetry in a parallelogram vary as per the type of parallelogram.
What Are Lines of Symmetry in a Parallelogram?
The lines of symmetry in a parallelogram are those lines that divide a parallelogram into two halves such that each half is the mirror image of the other. We know that there are different parallelograms categorized as per their shapes, the line segments, and corners they are made up of. Thus, these have different lines of symmetry and different numbers of symmetry lines. We can find whether a shape is symmetrical by folding it and checking for the Line of Symmetry. If the folded part sits perfectly on top, with all edges and corners matching, then the folded line represents a Line of Symmetry and that shape is symmetrical either along its length, breadth, or diagonals. Let's check for the lines of symmetry in a general parallelogram:
From the above figure, we can observe that:
- There is no line of symmetry of a parallelogram along its length, breadth. There is no superimposition of one half on the other when folded along its half.
- The diagonals are not symmetrical. This is because, when we fold the parallelogram along the diagonal line, we do not get the same shape as two halves.
Thus, the parallelograms have no lines of symmetry but they have rotational symmetry at 180°, about the center.
Symmetry Lines in Different Parallelograms
Different parallelograms are varied in their shape and so do their lines of symmetry.
Let's study them in detail.
| Parallelogram | Number of symmetry lines | Symmetry lines |
|---|---|---|
| Square | 4 | Both its diagonals and the lines joining the midpoints of its opposite sides, that is the bisectors. |
| Rectangle | 2 | The lines joining the midpoint of the opposite and parallel lines (i.e. the bisector) of the rectangle. |
| Rhombus | 2 | Both its diagonals dividing it into two identical halves. |
Rotational Symmetry of a Parallelogram
Rotational symmetry is when an object is rotated in a particular direction, that too around a point. So, when a shape is turned, and the shape is identical to the origin, rotational symmetry persists. The figure retains its exact appearance after it is rotated, around a center point. A parallelogram has zero or no line of symmetry. As per the order is concerned, it has rotational symmetry of order 2.
Different parallelograms have different orders of rotational symmetry:
- Square - 4 - 90°, 180°, 270°, 360°
- Rectangle - 2 - 180°, 360°
- Rhombus - 2 - 180°, 360°
Important Notes
- In Mathematics, symmetry exists when one shape is identical to the other shape when it is moved, rotated, or flipped.
- When a shape or an image looks exactly similar to the original shape or image after some rotation, that's rotational symmetry.
- An object and its image are symmetrical with reference to its mirror line.
Related Articles on Lines of Symmetry in a Parallelogram
Solved Examples on Lines of Symmetry in a Parallelogram
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Example 2: Check for the lines of symmetry in a rhombus.
Solution:
We know that a rhombus has 4 equal sides but what about diagonals? Are the diagonals also equal in length? The diagonals of a rhombus intersect at equal angles and thus makes four equal parts when folded along the lines of symmetry. Therefore, a rhombus has two lines of symmetry.
FAQs on Lines of Symmetry in a Parallelogram
Are there Any Lines of Symmetry in a Parallelogram?
A general parallelogram has no line of symmetry but different parallelograms, such as rectangle, square, or rhombus have lines of symmetry.
What Is a General Parallelogram?
In Euclidean geometry, a parallelogram is a quadrilateral with two pairs of parallel sides with the opposite sides being equal in length and the opposite angles being equal in measure.
Which Parallelogram has the Maximum Number of Symmetry Lines?
A square has 4 lines of symmetry that is the maximum amongst all other parallelogram types.
What Are the Symmetry Lines in Different Parallelograms?
The different parallelograms have a different number of symmetry lines
- A Square has symmetry lines along the diagonals, bisectors of opposite sides
- A Rectangle has symmetry lines along the bisectors of opposite sides
- A Rhombus has symmetry lines along the diagonals.
How Many Lines of Symmetry Does An Irregular Quadrilateral Have?
An irregular quadrilateral has no Lines of Symmetry.