Classifying two-dimensional shapes

Different categories of quadrilaterals - part 2

The most significant aspect of the angles of a parallelogram concerns whether or not they are right angled. If they are, then the shape is called a rectangle. Note that if one angle in a parallelogram is a right angle, because opposite angles are equal and the four angles add up to four right angles, all the angles must be right angles. The rectangle is probably the most important four-sided shape from a practical perspective, simply because our artificial world is so much based on the rectangle. It is almost impossible to look anywhere and not see rectangles.

Interestingly, however, there are children who grow up in rural areas of some African countries where their environment is based on the circle – they sit on circular stools in circular houses in circular villages – and this is often reflected in their relative confidence in handling the mathematics of circles and rectangles, compared with, say, Irish children. Then, a rhombus is a parallelogram in which all four sides are equal. A square  is therefore a rhombus that is also a rectangle, or a rectangle that is also a rhombus. It is, of course, a quadrilateral with all four sides equal and all four angles equal (to 90degrees), so ‘square’ is another name for a regular quadrilateral.