A parallelogram is a type of quadrilateral where the opposite sides are parallel and equal. The imaginaryline 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 ofa parallelogram refer to the lines cutting the parallelogram into two identical parts. Also, the lines of symmetry in a parallelogram varyas per the type of parallelogram.
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|1.||What AreLines of Symmetry in a Parallelogram?|
|2.||Symmetry Lines in Different Parallelograms|
|3.||Rotational Symmetry of a Parallelogram|
|4.||Solved ExamplesonLines of Symmetry in a Parallelogram|
|5.||Practice QuestionsonLines of Symmetry in a Parallelogram|
|6.||FAQs onLines of Symmetry in a Parallelogram|
What AreLines of Symmetry in a Parallelogram?
The lines of symmetry in a parallelogram are those lines that divide a parallelogram into two halves such thateach half is the mirror image of the other. We know that there are different parallelograms categorized as per their shapes, the linesegments, and corners they are made up of. Thus, these have different lines of symmetry and different numbers of symmetry lines. Wecan find whether a shape is symmetrical by folding it and checking for theLine of Symmetry. Ifthe folded part sits perfectly on top, with all edges and corners matching, then the folded line representsa 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 lineof symmetry of a parallelogramalong 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 parallelogramalong the diagonal line, we do not get the same shape as two halves.
Thus, the parallelograms have no lines of symmetry buttheyhave 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.
|Square||4||Both its diagonals and the lines joining the midpoints of its opposite sides, that is the bisectors.|
|Rectangle||2||The linesjoining the midpoint of the opposite and parallel lines (i.e. the bisector) of the rectangle.|
|Rhombus||2||Both its diagonalsdividingit 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 noline 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 NotesIn Mathematics, symmetry exists whenone shape is identical to the other shape when it is moved, rotated, or flipped.When ashape 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.
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Solved ExamplesonLines of Symmetry in a Parallelogram
Example 1:What are the angles at which a parallelogramhas rotational symmetry?
When a shape is turned, and the shape is still identical to the origin, then it can be said that it shows rotational symmetry. So, ifthe figure retains its exact appearance after it is rotated, around a center point. Thus, we can saythat aparallelogram showsa rotational symmetry at 180°.
Example 2: Check for the lines of symmetry in a rhombus.
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, arhombus has two lines of symmetry.
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Practice Questions on Lines of Symmetry in a Parallelogram
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FAQsonLines of Symmetry in a Parallelogram
Are there Any Lines of Symmetry in a Parallelogram?
A general parallelogram has no lineof symmetry butdifferent parallelograms, such asrectangle, 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 MaximumNumber of Symmetry Lines?
A square has 4 lines ofsymmetry 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 linesA Square has symmetry lines along thediagonals, bisectors of opposite sidesA Rectangle has symmetry lines along thebisectors of opposite sidesA Rhombus has symmetry lines along thediagonals.
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How Many Lines of Symmetry Does An Irregular Quadrilateral Have?
An irregular quadrilateral has no Lines of Symmetry.
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