9-5 Symmetry (Reflectional and Rotational)
Remember that a reflection is a transformation that flips an object over a given line, known as
the line of reflection, and a rotation is a transformation that turns an object around a fixed
point, known as the center of rotation.
A figure has ÿ if there exists a rigid motion (reflection, translation, rotation)
that maps.the figure onto itself.
- A figure in a plane has reflectional symmetry (line symmetry)
if the figure can be mapped onto itself by a reflection. The line in which the reflection takes
place in is known as the ÿÿi ÿ ÿ ÿ ÿ (or axis of symmetry).
Example 1: Determine if the fo!lowing figures have reflectional symmetry. If so, draw all lines
I
of symmetry.
A.
ÿ
B.
)ÿÿL S.'ÿÿrÿL - A figure in a plane has rotational symmetry (radial symmetry)
if the figure can Be mapped onto itself by a rotation between 0° and 360o about a fixed point.
The point in whichÿthe rotation takes place about is known as the ÿeÿ ÿ ÿÿ
(or point of symmetry).
The number of times the figure maps onto itself as it rotated from 0° to 360 is called the
The ÿ ÿ ÿ (or angle of rotation)is tÿe smallest angle in which a
figure can be rotated so that it maps back onto itself.
magnitude = 360o + order
Example 2: Determine if the following figures have rotational symmetry. If so, state the order
of symmetry and the magnitude of symmetry. Does the figure also have re?lectional symmetry?
A.
B.ÿ
q
C.