In its simplest definition, a quadrilateral is a geometrical form with four sides. The tricky part comes in when the shape shifts from a straightforward square to something that looks more like a kite or your dining room table.
Take trapezoids and isosceles trapezoids, for example. These quadrilaterals have only one pair of opposite sides parallel. A rhombus, a rectangle, and a parallelogram all have two sets of parallel sides, but they are not the same in appearance. Each figure has its own associated theorems that differentiate them.
Here are a few of many theorems that you'll use in geometry to determine a specific quadrilateral:
- Opposite angles of a parallelogram are equal.
- If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
- The diagonals of a rectangle are equal.
- The diagonals of a rhombus are perpendicular to one another.
By the way, a square has all the properties of the parallelogram and the rectangle and the rhombus; it's a quadrilateral with all right angles and all equal sides!