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Middle/High School Algebra, Geometry, and Statistics (AGS)
8.3 Symmetry Important Points

1. Line symmetry or Linear symmetry:

A figure is said to have line symmetry if there exists at least one line in the figure such that on folding the figure about this line, the two parts of it exactly coincide.  A line of symmetry divides the figure into two congruent parts.  A line segment is symmetrical about its perpendicular bisector.  An angle is symmetrical about its bisector.  An isosceles triangle is symmetrical about the bisector of the angle between equal sides.

FigureNo. of lines of symmetry
Isosceles Triangle1
Equilateral Triangle3
n sided regular polygonn
A circle is symmetrical about its diameter.

3. Point symmetry:

A figure is said to have point symmetry about a point 'O', if every line segment from the boundary of the figure is bisected by 'O'. The figure remains invariant under rotation about 'O', through 1800. The point 'O' is called the centre of symmetry. A parallelogram has point symmetry about the point of intersection of its diagonals.  A circle has point symmetry about its centre.

4. It is not necessary that every figure has a line of symmetry.  A figure may have more than one line of symmetry.  A figure and its image about a line are symmetric about the line.

Directions: Draw at least 10 figures of your own and identify the symmetry.