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A rectangle is formed of 2 lines of symmetry which divides it into two identical parts. A shape can be of different types of symmetry, such as linear symmetry, mirror symmetry, reflectional symmetry, and so on, and can be of two or more lines of symmetry. How many lines of symmetry are in a rectangle? If you have ever had that question while exploring shapes and you wondered about lines of symmetry in a rectangle then stay tuned. Regular shapes such as rectangles do have lines of symmetry on which they can be folded as equal parts. Therefore, a rectangle is also considered a special parallelogram, and for a rectangle, both the line and rotational symmetry exist. Let us know more about the lines of asymmetry in a rectangle.
Read Also: Rotation Formula
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Key takeaways: lines of symmetry, lines of symmetry in a rectangle, rotational symmetry, linear symmetry, mirror Symmetry, reflectional Symmetry.
What is the Line of Symmetry in a Rectangle?
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A figure, in geometry, is considered as one symmetrical figure If it can be divided into two identical equal parts with the help of a line. This dividing line of the figure is known as the line of symmetry. Now, some figures/shapes can have one while other shapes have more than one line of symmetry. Reflectional symmetry, rotational symmetry, linear symmetry are the main types of symmetry.
On the other hand, a rectangle is a polygon with four sides. The two opposite sides of a rectangle are equal and parallel to each other. That is what makes a rectangle different from a square. The diagonals of the rectangle are also equal with 90° angles always.
Check Also: Pair of Angles
How Many Lines of Symmetry Does a Rectangle Have?
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A rectangle, unlike a square, is not equal from all sides. But, its opposite sides are equal. Therefore, there are two lines of symmetry in a rectangle. One from its length and another from its breadth. Both these lines cut the rectangle into two mirror halves. Hence, if you keep one half over the other, it will cover the part as an equal one with zero dissimilarities.
Image 1
This image shows both the lines of symmetry in a rectangle. Hence, a rectangle has two lines of symmetry.
Now, one may ask if lines by the diagonals can also be the lines of symmetry in a rectangle. Like this:
Image 2
But, No! Because, if you cut a rectangle into two halves by its diagonal. Then, one half will not superimpose the other. Moreover, they won't be mirror halves. Hence, lines by diagonals can not be the lines of symmetry in a rectangle.
Check Important Notes for Analytical Geometry
Rotational Symmetry of a Rectangle
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A rectangle has two rotational symmetries, one at 180° and another at 360°. This means there are 2 times during rotation of 360° in the rectangle i.e., at 180° and 360°. Unlike, a square that has more than two rotational symmetries. (Note: A square has rotational symmetry of four according to its four equal sides in the figure.)
Things to remember
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- Lines of symmetry in a rectangle are two.
- There is linear symmetry and rotational symmetry in a rectangle.
- A rectangle is a four-sided polygon with two parallel and equal sides.
- The line of symmetry cuts the shape into two mirror halves.
Read More: Horizontal and Vertical Lines
Sample Questions
Ques: Find out whether line 1 and line 2 marked in the figure below are the lines of symmetry in a rectangle or not. Give the reason behind your answer. (2 marks)
Ans: No, line 1 and line 2 marked in the figure are not the lines of symmetry in the rectangle. If this or any rectangle is folded along any of these lines, the halves will not be the mirror halves. If you keep them over each other, one part will not superimpose the other. Hence, these lines are not lines of Symmetry in the rectangle.
Ques: At which angles does a rectangle have rotational symmetry?(2 marks)
Ans: A rectangle has rotational symmetry at two angles. one at 180° and the second at 360°. These are the rotational symmetries of a rectangle.
Ques: How many lines of Symmetry does a rectangle have? (2 marks)
a) 4
b) 3
c) 1
d) 2
Ans: Option d) 2 is the correct answer.
Explanation: A rectangle has two lines of symmetry. One at its length and second at its breadth.
Ques: Lines of symmetry of a rectangle cannot divide it ____ (2 marks)
a) Diagonally
b) Along with its length
c) Along with its breadth
d) None of these
Ans: Option a) Diagonally is correct.
Explanation: Lines of symmetry of a rectangle cannot divide it Diagonally. Because, if the rectangle is cut by diagonal. Then, the halves will not be able to superimpose each other. Unlike the one, they do when cut along with its breadth or length.
Ques: A rectangle has an order of rotational symmetry of 2 at ____ (3 marks)
a) 90° and 360°
b) 180° and 360°
c) 90° and 180°
d) None of these
Ans: Option b) 180° and 360° is correct.
Explanation: If we rotate a rectangle at 90°, it won't be like the shape it was before. Hence, we would rotate it again i.e., a rotation of 180° in total. If we then divide the rectangle, the parts will be symmetrically apt and equal shapes. Therefore, a rectangle has an order of rotational symmetry of 2 at 180° and 360°.
Ques: Rectangle is a ___. (2 marks)
a) Rhombus
b) Kite
c) Triangle
d) Quadrilateral
Ans: Option d) Quadrilateral is correct.
Explanation: Rectangle is a Quadrilateral because it has four sides, four vertices, and four angles.
Ques: If I fold a rectangle and then remove ¼ part from one side of the rectangle. Will the folded parts be the mirror halves now? (3 marks)
a) No, the parts are not equal and cannot be the mirror halves.
b) Yes, they are mirror halves.
c) Probably
d) None of the above
Ans: Option a) No, the parts are not equal and cannot be the mirror halves is the correct answer.
Explanation: Because, if one-fourth side of the rectangle is removed from one side. Then, it doesn't remain equal to the other side. Therefore, if we fold it, the parts will not be mirror halves and equal parts. Hence, option a is correct.
Ques: A square has four lines of Symmetry. A rectangle always has squares in it. Therefore, the rectangle should also have four or more lines of Symmetry? Yes/no. Justify your answer. (2 marks)
Ans: A square has four lines of Symmetry. A rectangle also has many small squares in it. But, if it comes to lines of Symmetry in a rectangle i.e., parts that will superimpose each other. Then, a rectangle has only two lines of Symmetry and not more than this.
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