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


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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