- It has two pairs of parallel sides.
- It has two pairs of equal sides.
- All its internal angles are right angles (90o), as shown by the small yellow squares.
- The diagonals also cross at right angles, as shown by the small grey squares.
In the following diagrams, the arrows indicate lines which are parallel. All the lines with just one arrow on them are parallel to all the other lines with just one arrow on them. All the lines with a double arrow on them are parallel to all the other lines with a double arrow on them.
Similarly, a dash on a line indicates lines of the same length. All the lines with just one dash on them are the same length as all the other lines with just one dash on them. All the lines with a double dash on them are the same length as all the other lines with a double dash on them.
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| A rectangle is similar to a square, except that it has two long sides and two short sides. It still has two pairs of parallel sides (the long sides are parallel to each other and the short sides are parallel to each other) and two pairs of equal sides (the long sides are equal to each other and the short sides are equal to each other), but the four sides are not equal to each other. |  |
One other difference - the diagonals definitely don't cross at right angles, unlike the square.
| A parallelogram is often thought of as a "rectangle pushed sideways." It has two parallel long sides the same length and two parallel short sides the same length, just as the rectangle does, except that the interior angles are not right angles (90o). Again, the diagonals definitely don't cross at right angles. |  |
| Just as a parallelogram is a rectangle that has been pushed sideways, so a rhombus is a "square pushed sideways". It has all the properties of a parallelogram - two pairs of parallel sides which are equal in length - except, in the case of a rhombus, all the sides are equal. Also, this time the diagonals do cross at right angles, as shown by the grey lines in the diagram. |  |
| These shapes have only one pair of parallel sides. It doesn't have to have any two sides the same length, and, although it is possible to draw a parallelogram which has its diagonals crossing at right angles, generally speaking, they don't. |  |
A parallelogram is a particular sort of trapezium where there are two pairs of parallel sides instead of just one. Similarly, a rhombus is a particular sort of parallelogram, and a rectangle is another particular sort of parallelogram. A square is a particular sort of rectangle and, at the same time, a particular sort of rhombus. This is summarised in the following Venn diagram:
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T = Set of all trapeziums P = Set of all parallelograms Re = Set of all rectangles Rh = Set of all rhombuses S = Set of all squares |
| These shapes were named after the toys that people with nothing better to do fly on windy days. They do have two pairs of equal sides, but these sides are not parallel to each other, i.e. the two shorter equal sides touch each other and the two longer equal sides touch each other. The two diagonals do cross at right angles, as shown in the diagram. |  |
| An arrow head is a concave quadrilateral, i.e. it has a dent in it. More mathematically, we say that one of the interal angles is a reflex angle (i.e. greater than 180o). This is the one defining characteristic of an arrowhead. |  |
| Any quadrilateral which doesn't fall into one of the seven categories above is termed a scalene quadrilateral. They generally have no angles equal, no sides equal (although it is just about possible to draw a scalene quadrilateral with two equal sides) and no sides parallel. |  |