There are three primary ways to move figures around without changing their size or shape: reflection, rotation and translation. If you can reflect or flip a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or line symmetry. The line that you reflect over is called the line of symmetry. A line of symmetry divides a figure into two mirror images halves. In these examples, the dashed lines are the lines of symmetry. Figures can have zero lines of symmetry or they can have an infinite number of lines of symmetry.
If you can rotate or turn a figure around a center point by 180 degrees or less and the figure appears unchanged then the figure has rotation symmetry. The point around which you rotate is called the center of rotation, and the smallest angle you need to turn is called the angle of rotation. A square has rotation symmetry at 90 degrees, because if you rotate the square 90 degrees it looks exactly the same. A regular pentagon has rotation symmetry at 72 degrees.
Plane symmetry occurs when a plane intersects a three dimensional object such that one half is the reflected image of the other half. Such a plane is imaginary and divides an object into two halves, each of which is the mirror image of the other in this plane. Plane symmetry is much like line symmetry only in three dimensions. Common objects displaying plane symmetry are rectangular solids, spheres, cones and boxes.
