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.
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
● Related Concepts
● Order of Rotational Symmetry
● 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
7th Grade Math Problems
8th Grade Math Practice
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