Geoboard Geometry
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while two sides remain constant, the other two, which are equal, increase as we pass from one figure to the next on the right.
If we start with a square, we can see that it does in some way belong to the series of four parallelograms; but the notion of identifying a square or a rectangle with a parallelogram requires care and attention and may take some time.
Fig. 8
This work can be repeated taking as the common side the two nails in the middle of one side of the board. A new feature, symmetrical pairs of parallelograms, results. If we cease to restrict ourselves to the next row of the lattice many more parallelograms can be obtained which could form the basis for another enquiry. This might be a study of diagonals and their property of bisecting each other. To give such a study its full value, it should be included in a general consideration of diagonals of quadrilaterals. It is already known that with one elastic band we can form:
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