Definition:Quadrilateral/Parallelogram

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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.

Parallelogram.png


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

  • Results about parallelograms can be found here.


Four day, five day marathon
We're moving like a parallelogram
-- Motorhead: Ian Kilmister


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 $22$)