Materials were written for an entire year's course in geometry in which transformations were used to develop the concepts of congruence, similarity, and symmetry, as well as being a vehicle for proof.

Transformations change the size or position of shapes. Scale factors can change the size of the shape. When a shape is translated, it is moved up or down and/or left or right. Every point in the shape ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

Sometimes a shape is transformed using more than one step, for example a reflection followed by a rotation. The combination of transformations can usually be described as a single transformation.