Quadrilaterals are classified by observable and definitional properties, including four sides, parallel or perpendicular sides, congruent side lengths, and right angles; relevant categories include trapezoids, parallelograms, rectangles, rhombuses, squares, and kites. The classification is hierarchical rather than mutually exclusive: every square is both a rectangle and a rhombus, and a rectangle or rhombus may be a parallelogram, regardless of orientation or appearance. Formal proofs and coordinate-based generalizations are not included.
A quadrilateral is a closed shape with exactly four sides. To classify one, look for these properties:
Classifications can overlap. For example, every square is also a rectangle, a rhombus, and a parallelogram.
Example: A quadrilateral has these properties:
Step 1: Check the number of sides.
It has four sides, so it is a quadrilateral.
Step 2: Check parallel sides.
Both pairs of opposite sides are parallel, so it is a parallelogram.
Step 3: Check the angles.
All four angles are right angles, so it is a rectangle.
Step 4: Check the side lengths.
All four sides are congruent, so it is a rhombus.
Step 5: Name the most specific classification.
A shape that is both a rectangle and a rhombus is a square.
So, this quadrilateral is a square. It can also be described as a rectangle, rhombus, and parallelogram because those classifications overlap.
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Earned ?