Symmetry

Line Symmetry. A dotted line has been drawn in this figure (Fig. 27). The figure is now divided into two parts that have the same size and shape. If the figure is folded on the dotted line, the two parts will coincide. We say that the figure is symmetrical about the dotted line. The dotted line is called the axis of symmetry.

It is possibly for a figure to have more than one axis of symmetry. In Fig. 27 line RS is an axis of symmetry. If we fold the figure along RS, the two parts will coincide. A point

on the left side will fall on only one point on the right side. Any two such points are called corresponding points. For example, A and B are corresponding points. AV is also an axis of symmetry. Then B and R are corresponding points. What is the third possible axis of symmetry? What two points will correspond when this axis is drawn?

Notice, if line AB is drawn, the axis of symmetry RS is perpendicular to, and bisects AB. If a figure has line symmetry, then the axis of symmetry must be perpendicular to the line joining every two corresponding points and must also bisect it.

Point Symmetry. If a dotted line is drawn from any one point on the figure above to any corresponding point, the dotted line will be bisected in the point 0. The figure has balance about point 0 and is therefore, an example of point symmetry. Point 0 is called the centre of symmetry (Fig. 28).

If a figure has point symmetry, then the line which con­nects every two corresponding points must pass through the centre of symmetry and be bisected by it.

It is possible for a figure to have both point symmetry and line symmetry. An example is the circle. Any diameter will be an axis of symmetry. Hence the circle possesses line symmetry.

Pick any point A on a circle. Connect this point with cen­tre 0. Extend this line to a point B, on the other side of the circle. The radius OA is equal to the radius OB. Because this is true of any line drawn through 0 and bounded at either end by the circle, 0 is the centre of symmetry and the circle possesses point symmetry as well as line symmetry.

Plane Symmetry. If a solid can be divided into two equal solids by a plane, and if every part on one side of the plane has a corresponding part on the other, the original solid has plane symmetry.