Symmetry

• Symmetry refers to the exact match in shape and size of two halves of an object, split along an axis.
• Two types of symmetry are: line symmetry (reflexion symmetry) and rotational symmetry.
• An object has line symmetry if a line can be drawn dividing it into two mirror images. This line is known as the line of symmetry or axis of symmetry.
• An object has rotational symmetry if it can be rotated about a point and still looks the same. The number of times it fits onto itself in one full turn (360 degrees) is called the order of rotational symmetry.
• Regular polygons (shapes with all sides and angles equal) have equal numbers of lines of symmetry and orders of rotational symmetry. For example, a regular pentagon has 5 lines of symmetry and rotational symmetry of order 5.
• Irregular polygons may have no lines of symmetry or may have one or more lines, but these numbers are not equal.
• Reflections can be performed using mirror lines. The original object is referred to as the ‘object’ and the resulting symmetrical image is the ‘image’.
• In a reflexion, the object and its image are equidistant from the mirror line.
• A shape’s symmetry properties can help determine other features, such as tessellation. For example, regular polygons tessellate because of their symmetry.
• In transformations, an object’s symmetry can help predict features of the image. For example, a reflexion maintains the size, shape and orientation of an object.
• Recognition of symmetry is also helpful in sketching graphs of functions. Many mathematical functions have symmetry.
• To measure symmetry one uses a protractor or gridded paper to ensure precise lines and angles.
• The concepts of symmetry also apply in three dimensions. Three-dimensional symmetry involves rotation and reflexion using a plane, line or point.