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.

The lengths of the larger square are three times the length of the smaller square. The area of the larger square is nine times as large as the area of the smaller square. The area scale factor is 9.

A new 13-sided shape is the first example of an elusive "einstein" — a single shape that can be tiled infinitely without repeating a pattern. When you purchase through links on our site, we may earn ...