Lines of Symmetry in a Rectangle

Lines of symmetry are the lines that run through a shape thereby splitting the shape into two identical parts that fit perfectly on each other when folded. For a shape to be identified as an asymmetrical figure, it must have at least one line of symmetry. A shape or figure can have one or more lines of symmetry depending on its nature. When a shape is folded along its line of symmetry, the two halves would be superimposed on each other perfectly.

If you want to visualize the lines of symmetry of any shape, take a piece of paper, cut it in a shape you would like to experiment with, and fold it along the possible lines of symmetry. If the two sides sit perfectly on each other, you’ve got your line of symmetry. We will now further identify the lines of symmetry in a rectangle. 

What do you Mean by Line of Symmetry?

A line of symmetry is a line that passes through a shape, which divides the shape into two identical parts and when folded it fits perfectly. At least one line of symmetry is required for the shape to be identified as a symmetric shape. A shape or shape can have one or more lines of symmetry, depending on its nature. If the shape is folded along a line of symmetry, the two halves are perfectly overlapped. 

If you want to visualize a line of symmetry of any shape, take a piece of paper, cut it into the shape you want to experiment with, and fold it along the possible lines of symmetry. When the two sides completely overlap, a line of symmetry is created. Then further identify the rectangular symmetry line. 

Line of Symmetry of a Rectangle 

The rectangle has two lines of symmetry and is divided into two identical parts. Shapes can have different types of symmetry, like Linear symmetry, mirror symmetry, reflection symmetry, etc. The shape can consist of two or more lines of symmetry. A rectangle is also one of a quadrilateral whose two opposite sides are equally parallelograms. Therefore, a rectangle is also considered a special parallelogram.

In a rectangle, the opposite sides are the same and are parallel to each other, and the adjacent sides are at right angles. Therefore, it can be folded once along the length and once along the width. This will give you two lines of symmetry. The length of a rectangle is always longer than its width, so when folded diagonally, the two halves do not completely overlap and hence we do not get the matching shapes. The folded half right-angled corners (half resembling a right triangle) are separated from each other and misaligned. Therefore, the diagonal is not a rectangular symmetry line.
We can hence say that a rectangle has two lines of symmetry. 

Rotational Symmetry of a Rectangle

When a shape or plane shape rotates around its axis and looks the same as before,  it is called rotational symmetry. In other words, there is rotational symmetry if the shape remains the same even if it is partially rotated. A rectangle becomes rotationally symmetric when rotated 180 ° and 360 ° around its axis. Rotate the rectangle and it will fit the border exactly twice. One time it was 180 ° and the other time it was 360 °. For a rectangle, the length is greater than its width, so it can be said that there is no rotational symmetry at 90 ° and 270 °.

How Many Lines of Symmetry Does a Rectangle have?

In a rectangle, the opposite sides are equal and parallel to each other and the adjacent sides are at a right angle. Thus, it can be folded one along its length, and once along its breadth, giving us two lines of symmetry. The sides would superimpose only when folded along these lines. The below image depicts two lines of symmetry of a rectangle.

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Since the length of a rectangle is always longer than its breadth, folding along the diagonals would not result in a perfect superimposition of two halves. The right-angle corners of the folded halves (the haves would resemble a right-angled triangle) would be apart from each other, misaligned. Thus the diagonals are not lines of symmetry for a rectangle.

How Many Lines of Symmetry does a Square have?

So now that we know how many lines of symmetry a rectangle has, now let’s take a quick look at another quadrilateral, a square. For a square, all of its sides are equal, opposite sides are parallel to each other and the adjacent sides are at a 90°. Thus, in addition to the two lines of symmetry lines like that of a rectangle, a square also has symmetry lines along its diagonals. (As the diagonals would split the square into two right-angled isosceles triangles that would sit perfectly on top of each other.)

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The above image shows all the lines of symmetry a square has, folding along any of these lines would result in two identical halves that fit on each other. 

Do it Yourself

Take a piece of paper, draw a rectangle on it, and cut it out. Mark the center points along its length and breadth. Draw two symmetrical lines along these lines. Now fold the paper along these lines. You will notice that the two halves are identical and cover each other perfectly.

Now try folding along the diagonals to see the corners misaligned. Use a similar exercise for squares, triangles, and any other shapes that you want to experiment with.