What a quadrilateral is

This chapter is about four-sided figures, called quadrilaterals. The word comes from Latin: quadri means four, and latus means side.

A quadrilateral is a closed figure made of four straight sides. Not every figure with four lines counts. Look closely at the ones that fail: the sides may cross, a 'side' may be curved instead of straight, or the figure may not close up.

The angles of a quadrilateral are the angles between its sides, so it has four of them, one at each corner (and four corners, or vertices).

We start with the most familiar ones: rectangles and squares.

Rectangle: a rectangle is a quadrilateral in which

• (i) the angles are all right angles (90°), and
• (ii) the opposite sides are of equal length.

Notice what a definition is for. It 'precisely states the conditions a quadrilateral has to satisfy to be called a rectangle'. It's a test to pass, not a description of how a rectangle looks. Any shape passing both tests is a rectangle, however it's drawn or turned; any shape failing either test is not, however much it looks like one.

That raises the question this chapter keeps coming back to: are there other ways to define a rectangle? Could a different set of conditions pick out exactly the same shapes? As you'll see, the answer is yes, and one of the other definitions is the one carpenters actually use.