There are three types of symmetry: reflectional, rotational and translational symmetry. Reflectional symmetry is also known as mirror or line symmetry.
When a reflected image is flipped over horizontally, it is a horizontal reflection. A figure with horizontal symmetry has a vertical axis of reflection. The two sides of the human body are a horizontal reflection of one another. The human body has a vertical axis of reflection. When printed, the capital letter "A" has a vertical axis of reflection, and is therefore an example of a horizontal reflection.
If a shape is flipped over vertically, it is a vertical reflection. Figures with vertical symmetry have a horizontal axis of reflection. When printed, the capital letter "E" has a horizontal axis of reflection and is an example of a vertical reflection. A regular diamond shape is an example of a vertical reflection and has a horizontal axis of reflection.
In a line reflection, the preimage -- or original image -- is reflected across a line of symmetry in the form of an image. Each point on the image is the same distance away from the line of reflection as the corresponding point on the preimage. The result is a figure that is congruent to the preimage known as an isometry. Congruent means the two shapes are the same size, the angles are the same and the line segments are the same length. A person's image in a mirror is a line reflection.
When an image is reflected across a single point rather than a line of symmetry, this is known as "point reflection." The center of the figure is a single point. For each point on one side of the figure, there is a corresponding point on the opposite side of the point of reflection. With a point reflection, the resulting image is congruent to the preimage.
A glide reflection is a combination of a translation -- also known as a slide or glide -- and a reflection. A translation is simply a movement of the shape up, down or sideways without changing the orientation of the shape. Applying both these transformations to the same shape, one after another, is known as a composition of transformations.