You have landed on the right page to learn about Figures with Multiple Lines of Symmetry. In geometry, symmetry is described as a balanced and proportionate likeness between the two sides of an object. It signifies that one half is the inverse of the other. The line of symmetry is an imaginary line or axis along which you can fold a figure to generate symmetrical halves.

The mirror line or axis of symmetry is another name for the line of symmetry. If a shape or an object can be divided into two identical pieces, it exhibits symmetry. One side of a symmetrical object is the mirror image of the other. Few shapes like spheres, circles, and regular polygons have multiple lines of symmetry. Continue reading to learn more about Figures with Multiple Lines of Symmetry.

What is Symmetry in Simple Words?

Symmetry is a concept that is frequently used in everyday life. When we encounter figures with evenly balanced proportions, we call them symmetrical. Peek at the image of the Taj Mahal and the India Gate below. Because of their symmetry, these photographs of architectural marvels are magnificent.

If we could fold an image in half to match the left and right parts, we would call it line symmetry. The two sections are mirror images of each other, as can be seen. If we lay a mirror on the fold, the image of one side of the photo will fall perfectly on the opposite side. The fold, which is the mirror line, becomes a line of symmetry (or an axis of symmetry) for the picture when this happens.

Figures With Unlimited Lines of Symmetry

Vertical, horizontal, or diagonal lines can be used as lines of symmetry. The square, for example, has four symmetry lines: two diagonals, vertical line, and horizontal line. Some figures have an infinite number of symmetry lines. A circle can have an infinite number of symmetry lines or none. All its diameters are symmetrical.
A circle has an infinite number of symmetry lines since there are unlimited lines through the center. This means that the circle’s areas on both sides of the line must be the same. As a result, the symmetry line divides the circle into two halves with equal area.

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Figures with Two Lines of Symmetry

Two lines of symmetry: Two lines can be used to divide a figure into two equal sections. Two lines of symmetry are thought to exist in these shapes. Two lines of symmetry may be seen in the rectangle. The two symmetrical parts of a rectangle can be separated vertically, horizontally, or diagonally.
Here are a few examples for two lines of symmetry:
The symmetry of a rhombus: There are two lines of symmetry along the diagonals of a rhombus.

In rhombus \(PQRS\), diagonals \(PR\) and \(QS\) are two lines of symmetry.
The symmetry of rectangle: Two lines of symmetry run along the line segments connecting the mid-points of the opposite sides of a rectangle.

In rectangle \(ABCD\), \(PQ\) and \(RS\) are two lines of symmetry.
In English alphabets, the following letters have two lines of symmetry:

Example of Figures with Multiple Lines of Symmetry

There are several figures in which the symmetry lines can be more than \(2\). Regular polygons are symmetrical beauties, and their symmetry lines are interesting. We’ll talk about the symmetry lines of certain regular polygons in this section. If a polygon’s sides are of equal length and all its angles are of equal measure, it is said to be regular.

Equilateral triangle symmetry lines: All sides of an equilateral triangle have the same length, and each angle is \(60^\circ\). It has three lines of symmetry running through its three medians.

Lines of symmetry of a square: A square is a quadrilateral with all sides equal and each of its angles being right-angle, i.e. \(90^\circ\). A square’s diagonals are perpendicular bisectors of each other.
A square has four lines of symmetry, two diagonals and two-line segments connecting the mid-points of opposite sides.

Symmetry lines of a regular pentagon: All the sides of a regular pentagon are the same length and each of the measures of the angle \(108^\circ\). A regular pentagon has five symmetry lines.

Line symmetry of a regular hexagon: All the sides of a regular hexagon are equal, and each of the measures of the angle \(120^\circ\). A regular hexagon has six symmetry lines—three along the diagonals and three connecting the mid-points of opposite sides.

Use of Figures with Multiple Lines of Symmetry

1. We see symmetry in many places throughout our daily lives without even realising it. It can be seen in a variety of works of art, structures, and monuments. Nature uses symmetry to beautify her creations. Consider the images of the butterfly and the leaf, for example.
2. Multiple lines of symmetry are used to create patterns in painting.
3. Symmetry helps build beautiful buildings and monuments.

Solved Examples- Figures with Multiple Lines of Symmetry

Q.1. The letters \(A,\;B,\;C\) and \(D\) of the English alphabet are symmetrical about a line. Identify a line of symmetry in each case.
Ans: The line symmetry of the letters \(A,\;B,\,C\) and \(D\) are as follows:

Q.2. What other name can you give to the line of symmetry of
i. An isosceles triangle?
ii. A circle?
Ans: i. An isosceles triangle has one line of symmetry. One line of symmetry runs through the vertex of an isosceles triangle’s median from the vertex containing the equal sides. And another name of the line of symmetry of an isosceles triangle is altitude.

ii. A circle has an infinite number of symmetry lines due to the infinite number of lines that pass through the center. This indicates that the circle’s sections on both sides of the line must be the same size. So, the other name of the line of symmetry of a circle is the diameter.

Q.3. Identify three examples of shapes with no line of symmetry.
Ans: Shapes like a scalene triangle, a quadrilateral, and a parallelogram has no line of symmetry.

Q.4. State the number of lines of symmetry for the following figures:
i. An equilateral triangle
ii. An isosceles triangle
iii. A scalene triangle
iv. A rectangle
Ans: i. An equilateral triangle has three lines of symmetry. An equilateral triangle has the same length on both sides and the same measure on each angle. Three lines of symmetry connect the three medians of an equilateral triangle.

ii. An isosceles triangle has one line of symmetry. The median through the vertex containing the equal sides of an isosceles triangle has one line of symmetry.

iii. The number of lines of symmetry in a scalene triangle is zero because it has no equal sides and angles.

iv. A rectangle has two lines of symmetry. Two lines of symmetry run along the line segments connecting the mid-points of the opposite sides of a rectangle.

Q.5. Draw a line of symmetry for the shape octagon (has eight equal sides).
Ans: A figure is divided into identical sections by symmetry lines. A regular octagon has eight lines of symmetry, as we can see.

Summary

In this article, we learned about the definition of symmetry in simple words, the figures that have unlimited lines of symmetry, figures with two lines of symmetry, the example of figures with multiple lines of symmetry. We also saw the uses of figures with multiple lines of symmetry, solved examples on figures with multiple lines of symmetry, and FAQs on figures with multiple lines of symmetry.

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Frequently Asked Questions- Figures with Multiple Lines of Symmetry

Q.1. What are the 4 types of symmetry?
Ans: Translation symmetry, rotation symmetry, reflection symmetry, and glide reflection symmetry are the four primary types of symmetry.

Q.2. Which shapes have multiple lines of symmetry?
Ans: There are several figures with more than two lines of symmetry. Regular polygons are symmetrical beauties, and their symmetry lines are interesting. Regular polygons like an equilateral triangle, square, pentagon, hexagon, etc., have multiple lines of symmetry.

Q.3. What is another name of the line of symmetry?
Ans: The mirror line or axis of symmetry is another name for the line of symmetry.

Q.4. What are symmetrical figures in math?
Ans: If a shape or object can be divided into two identical pieces, it exhibits symmetry. One side of a symmetrical object is the mirror image of the other. The line of symmetry is the imaginary axis or line along which the figure can be folded to generate the symmetrical halves.

Q.5. Which figure has unlimited lines of symmetry?
Ans: A circle can have an infinite number of symmetry lines. An infinite number of diameters can be drawn in a circle. Each of these diameters divides a circle into two identical halves. Hence, these infinite number of diameters in a circle are an infinite number of lines of symmetries in a circle.