Have you ever noticed that when you place a picture on a photocopier turned one way the copy comes out flipped upside down? Have you ever tried to enlarge a copy of an object to fit into an special frame, and had to enlarge it several times before you got the size "just right?" Have you ever made a photocopy of a book cover or of your hands? Well, if you have witnessed or experienced any of these things, then you have been involved in some of the everyday mathematics that surrounds us.

Congruency, Similarity, and Nonsimilarity

The photocopier can produce copies that have virtually the same size as the original item copied. The two objects—original and its copy—are said to be mathematically congruent to each other. Two 2-dimensional objects are congruent if the objects have the same shape and the same size. On the photocopier...