The screens for smartphones, laptops, and televisions are all rectangular and constructed from four straight lines, which makes them quadrilaterals. In addition to those rectangular screens, you can use four straight lines to make many different shapes. Check out the figures below to see other shapes you can make by using four straight lines.
You can see that each of these figures is a quadrilateral, but what else do they all have in common? In other words, what are their properties?
| Properties of Quadrilaterals |
| 1. Quadrilaterals have exactly 4 straight sides. |
| 2. Quadrilaterals have exactly 4 vertices. |
| 3. Quadrilaterals have exactly 2 dimensions. |
While any two-dimensional figure with exactly four straight lines and exactly four vertices is classified as a quadrilateral, several quadrilaterals have special properties and special names. Rectangles and squares, for instance, are special quadrilaterals. You can recognize them easily after a lifetime of seeing them around you, but do you understand the geometric properties that define the special quadrilaterals? Compare what you already know to the properties described on the slides below.
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A quadrilateral is a square if all four sides have equal length and all four vertices are right angles.
A rectangle has four right angles and opposite sides that are the same length.
A trapezoid has two sides that are parallel and two sides that are not parallel.
A kite is a quadrilateral with adjacent sides that are the same length.
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel to each other.
The rhombus is a quadrilateral that is similar to a square but with slanted sides. A quadrilateral is a rhombus if all sides have equal length and opposite interior angles are equal. |
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Quadrilaterals are classified by their interior angles, the lengths of their sides, and the relationship of the sides with each other. Some quadrilaterals have four right angles, such as the square and rectangle. Other quadrilaterals, like the kite and trapezoid, have no right angles. Some quadrilaterals have parallel sides, while others do not.
Question
A square fits the definition of several different quadrilaterals. What are the different ways you can classify a square?
