A plane of symmetry cuts a shape in half so that on each side of the plane is a mirror image of the other side. Many shapes have planes of symmetry, including all prisms – shapes that have a constant cross section. This plane of symmetry of a prism is halfway along the prism, as shown below.
Cylinders can be thought of as prisms, with a circular cross section. As well as a plane of symmetry halfway along the cylinder, we can cut the cylinder lengthwise in may different ways, as long as the plane of symmetry passes though the centre of the circle at either end.
Cubes have many planes of symmetry. Two are shown below to the right.