GMAT Exam: A Simple Guide To Geometry - Quadrilaterals

Descriptions of Quadrilaterals

- trapezoid is a quadrilateral that has at least one pair of parallel sides.

Some authors define a trapezoid as a quadrilateral that has only one pair of parallel sides.

- parallelogram is a quadrilateral whose opposite sides are parallel and congruent.


- rhombus is a parallelogram that has four congruent sides.


- rectangle is a parallelogram that has four interior right angles.


- square is a parallelogram that has four interior right angles and four congruent sides.
It is a rectangle that has four congruent sides.
You also might say that it is a rhombus that has four interior right angles.

Useful Information About Quadrilaterals
- If a quadrilateral’s diagonals bisect each other, the quadrilateral is a parallelogram.
- If a quadrilateral has two sides that are parallel and congruent, the quadrilateral is a parallelogram.
- The diagonals of a rectangle or square are congruent.
- The diagonals of a rhombus or square are perpendicular to each other.
- If a quadrilateral’s diagonals are perpendicular bisectors of each other, the quadrilateral is a rhombus.
- A parallelogram that has one interior right angle has four interior right angles and is a rectangle.
- Consecutive angles of a parallelogram are supplementary.