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:

Line Segment Symmetry

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


2. An angle:

An Angle Symmetry

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


3. An isosceles triangle:

An Isosceles Triangle Line Symmetry

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:

Semi-circle Line Symmetry

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


5. Kite:

Kite Line Symmetry

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


6. Isosceles trapezium:

Isosceles Trapezium Line Symmetry

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:

Rectangle Line Symmetry

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:

Rhombus Line Symmetry

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:

Equilateral Triangle Line Symmetry

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


10. Square:

Square Line Symmetry

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


11. Circle:

Circle Line Symmetry

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.

Letters having One Line of Symmetry


Letter having both horizontal and vertical lines of symmetry:

H I X have two lines of symmetry.

Letter having 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.

Letter having No Line 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.

Letters having Infinite Lines of Symmetry

Lines of Symmetry


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





7th Grade Math Problems

8th Grade Math Practice

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