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 a symmetrical 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. 

How many Lines of Symmetry does 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 its 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 halves would resemble a right-angled triangle) would be apart from each other, misaligned. Thus the diagonals are not lines of symmetry for a rectangle.

Rotational Symmetry of a Rectangle

Rotational symmetry is when a shape fits perfectly on itself when it is rotated partially. If it only fits after a full rotation, then the shape has no rotational symmetry. If it fits at every fraction of rotation then it has infinite rotational symmetry. (A circle has an infinite rotational symmetry.)  

When you rotate a rectangle, it superimposes on itself twice, once at 180° and one at a whole 360°. Thus a rectangle has rotational symmetry of 2. Since the length of a rectangle is always more than its breadth, it would not fit on itself at 90° or 270°.

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

FAQ (Frequently Asked Questions)

1. Rectangle has how many lines of symmetry?

A rectangle has two lines of symmetry, one that is parallel to its length and one that is parallel to its breadth. The two halves of a rectangle would fit perfectly on top of each other when it is folded along these lines. 

Unlike a square, the diagonals of the rectangle are not lines of symmetry as the sides of a rectangle are not all equal. 

2. What is the rotational symmetry of a rectangle?

A rectangle has rotational symmetry of 2, meaning it fits on itself twice when it’s being rotated. It fits at 180° and at a full rotation i.e. 360°.