Lines of Symmetry

Learn about lines of symmetry in different geometrical shapes.

It is not necessary that all the figures possess a line or lines of symmetry in different figures.

Figures may have:

No line of symmetry

1, 2, 3, 4 …… lines of symmetry

Infinite lines of symmetry

Let us consider a list of examples and find out lines of symmetry in different figures:

1. Line segment:

In the figure there is one line of symmetry. The figure is symmetric along the perpendicular bisector l.

2. An angle:

In the figure there is one line of symmetry. The figure is symmetric along the angle bisector OC.

3. An isosceles triangle:

In the figure there is one line of symmetry. The figure is symmetric along the bisector of the vertical angle. The median XL.

4. Semi-circle:

In the figure there is one line of symmetry. The figure is symmetric along the perpendicular bisector l. of the diameter XY.

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5. Kite:

In the figure there is one line of symmetry. The figure is symmetric along the diagonal QS.

6. Isosceles trapezium:

In the figure there is one line of symmetry. The figure is symmetric along the line l joining the midpoints of two parallel sides AB and DC.

7. Rectangle:

In the figure there are two lines of symmetry. The figure is symmetric along the lines l and m joining the midpoints of opposite sides.

8. Rhombus:

In the figure there are two lines of symmetry. The figure is symmetric along the diagonals AC and BD of the figure.

9. Equilateral triangle:

In the figure there are three lines of symmetry. The figure is symmetric along the 3 medians PU, QT and RS.

10. Square:

In the figure there are four lines of symmetry. The figure is symmetric along the 2diagonals and 2 midpoints of opposite sides.

11. Circle:

In the figure there are infinite lines of symmetry. The figure is symmetric along all the diameters.

Note:

Each regular polygon (equilateral triangle, square, rhombus, regular pentagon, regular hexagon etc.) are symmetry.

The number of lines of symmetry in a regular polygon is equal to the number of sides a regular polygon has.

Some figures like scalene triangle and parallelogram have no lines of symmetry.

Lines of symmetry in letters of the English alphabet:

Letters having one line of symmetry:

A B C D E K M T U V W Y have one line of symmetry.

A M T U V W Y have vertical line of symmetry.

B C D E K have horizontal line of symmetry.

Letter having both horizontal and vertical lines of symmetry:

H I X have two lines of symmetry.

Letter having no lines of symmetry:

F G J L N P Q R S Z have neither horizontal nor vertical lines of symmetry.

Letters having infinite lines of symmetry:

O has infinite lines of symmetry. Infinite number of lines passes through the point symmetry about the center O with all possible diameters.

Lines of Symmetry

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● Related Concepts

● Linear Symmetry

● Point Symmetry

● Rotational Symmetry

● Order of Rotational Symmetry

● Types of Symmetry

● Reflection

● Reflection of a Point in x-axis

● Reflection of a Point in y-axis

● Reflection of a point in origin

● Rotation

● 90 Degree Clockwise Rotation

● 90 Degree Anticlockwise Rotation

● 180 Degree Rotation

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7th Grade Math Problems

8th Grade Math Practice

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