How Many Lines Of Symmetry Are There In A Parallelogram?

In mathematics, symmetry occurs when one form is moved, rotated, or flipped and remains similar to the other. The Greek phrase “parallelogrammon,” which means “bounded by parallel lines” is where the name “parallelogram” comes from. As a result, a parallelogram is a quadrilateral with parallel lines on all sides. It’s a form with parallel and equal sides on both sides. Parallelograms are divided into three types: square, rhombus, and rectangle, each with its own set of characteristics. The line of symmetry is an imaginary line established along which you can fold a figure to produce the symmetrical halves. As a result, a parallelogram’s lines of symmetry refer to the lines that divide the parallelogram into two identical sections. In addition, the symmetry lines in a parallelogram differ depending on the type of parallelogram. Let us go into this in a little detail.

PARALLELOGRAM

A parallelogram is a type of quadrilateral created by parallel lines. A parallelogram’s angle between neighboring sides can vary, but the opposing sides must be parallel to be considered a parallelogram. If the opposing sides of a quadrilateral are parallel and congruent, it is a parallelogram. As a result, a parallelogram is defined as a quadrilateral with parallel and equal sides on both sets of opposing sides.

LINES OF SYMMETRY IN A PARALLELOGRAM

The lines that divide the parallelogram into two halves, each of which is the mirror image of the other, In a parallelogram, are known as the lines of symmetry. We know that parallelograms are classified according to their forms, line segments, and corners. As a result, they have distinct symmetry lines and varying numbers of symmetry lines. By folding a form and looking for the Line of Symmetry, we may determine if it is symmetrical. If the folded section fits exactly on top, with all edges and corners matching, the folded line is a Line of Symmetry, and the form is symmetrical in length, width, or diagonals. Let us look at the lines of symmetry in a general parallelogram, in the following image.

We can observe in the figure given above, that — A parallelogram has no symmetry line running along its length or width. When folded along its half, there is no superimposition of one half on the other; The diagonals aren’t even close to being symmetrical. This is because we don’t obtain the same form as two halves when we fold the parallelogram along the diagonal line. Therefore, the parallelograms do not have lines of symmetry, but they do exhibit rotational symmetry at 180 degrees around the center.

DIFFERENT PARALLELOGRAMS AND THE SYMMETRY LINES IN THEM

As mentioned earlier, there are three different types of parallelograms, and they vary in their lines of symmetry as well as their shape. The types are — square, rectangle, and rhombus. Let us study these parallelograms in a little detail.

Square — A parallelogram that has four equal sides and four right angles is known as a square. The number of lines symmetry in a square is 4. The symmetry lines are the bisectors, which are the diagonals and the lines connecting the midpoints of its opposite sides.

Rectangle — A parallelogram with two pairs of equal and parallel opposite sides and four right angles is known as a rectangle. The number of lines of symmetry in a rectangle is 2. They symmetry lines are the bisectors or the parallel lines and the lines that connect the midpoints of the rectangle’s opposing.

Rhombus — A parallelogram with four equal sides in which the opposite angles are equal is known as a rhombus. The number of symmetry lines in a rhombus is 2. The lines of symmetry are both its diagonals which divide it into two equal identical halves.

ROTATIONAL SYMMETRY OF A PARALLELOGRAM

When an item is rotated in a certain direction around a point, it is said to have rotational symmetry. Rotational symmetry is maintained when a form is twisted and the shape is identical to the origin. After being rotated around a center point, the figure keeps its exact look. A parallelogram has no or only one symmetry line. It possesses rotational symmetry of order 2 when it comes to order. It is important to note that different parallelograms gave different ordered od rotational symmetry, like the rotational symmetry of a square can be given as, square — 4–90o, 180o , 270o, 360o. Similarly, we can write the ordered of rotational symmetry for a rectangle as, rectangle — 2–180o, 360o; and the rotational symmetry for the rhombus can be given as, rhombus — 2–180o, 360o.

If you want to learn more about symmetry and parallelograms, or any other such interesting topics, just head on over to www.doubtnut.com where you will find the best information available, delivered to you by experts.