# Definition:Quadrilateral/Parallelogram

## Definition

A **parallelogram** is a quadrilateral whose opposite sides are parallel to each other, and whose sides *may or may not* all be the same length.

### Base

In a given parallelogram, one of the sides is distinguished as being the **base**.

It is immaterial which is so chosen, but usual practice is that it is one of the two longer sides.

In the parallelogram above, line $AB$ is considered to be the **base**.

### Altitude

An **altitude** of a parallelogram is a line drawn perpendicular to its base, through one of its vertices to the side opposite to the base (which is extended if necessary).

In the parallelogram above, line $DE$ is an **altitude** of the parallelogram $ABCD$.

The term is also used for the length of such a line.

## Also see

- Rectangle is Parallelogram: a rectangle is a
**parallelogram**all of whose angles are equal to a right angle.

- Altitude of Rectangle: the altitude of a rectangle is equal to one of its sides which is adjacent to its base.

- Results about
**parallelograms**can be found**here**.

## Euclid's Definitions

In the words of Euclid:

*Of quadrilateral figures, a***square**is that which is both equilateral and right-angled; an**oblong**that which is right-angled but not equilateral; a**rhombus**that which is equilateral but not right-angled; and a**rhomboid**that which has its opposite sides equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called**trapezia**.

(*The Elements*: Book $\text{I}$: Definition $22$)

## Heading text

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**parallelogram** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**parallelogram** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**parallelogram** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**parallelogram**