Definition of a Parallelogram

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.

A parallelogram is a quadrilateral
whose two pairs of opposite sides are parallel.

Example

If OPQR is a parallelogram, find the coordinates of point Q. P(1, 4), Q(a, b), R(6, 2).

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

If OPQR is a parallelogram, find the coordinates of point Q. P(1, 4), Q(a, b), R(6, 2).

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.