# Definition of a Parallelogram

How to solve the definition of a parallelogram problems: example, and its solution (2 ways).

## Definition

A parallelogram is a quadrilateral

whose two pairs of opposite sides are parallel.

## Example

By the definition of a parallelogram,*OR* // *PQ*.

So their slopes are the same.

This means the changes of the coordinates

in *OR* and *PQ* are the same: (+6, +2).

So *Q*(*a*, *b*) = (1 + 6, 4 + 2).

Solving this way is easier than setting

(slope of *OR*) = (slope of *PQ*).

## Example: Another Solution

Of course you can use the other pair of parallel lines:*OP* and *RQ*.

Their slopes are the same.

So the changes of the coordinates

in *OP* and *RQ* are the same: (+1, +4).

So *Q*(*a*, *b*) = (6 + 1, 2 + 4).

The answer is the same.