Congruence
Congruence is the basic concept of symmetry. In mathematics class, we explore this concept on a geoboard by trying to find ways to divide the board into two identical parts with rubber bands (hence, we must connect pin-to-pin). Here are a couple of examples, try to find some more...
What observations can you make about the two parts of the divided geoboard? About the lines that divide the area into two parts? What's the largest number of parts into which we could divide the geoboard?
Shapes which are exactly the same size and shape are called congruent shapes. All of the geoboards above have been divided into two congruent parts. It might seem easy to divide the square into congruent parts; here are a couple of challenges. Try to divide these shapes into congruent parts...
Now try these...
How the congruent parts of a shape are related determines the symmetry of the shape. Go to the Symmetry page to learn more...