Ctrl+k

Classify quadrilaterals

A quadrilateral is a closed shape with exactly four straight sides and four vertices; it can be classified by attributes such as equal side lengths, right angles, and pairs of parallel sides. The classification includes recognizing overlapping categories—for example, a square is both a rectangle and a rhombus—and understanding that a shape’s orientation or size does not change its classification. Formal proofs, diagonal properties, and angle-sum generalizations are beyond this scope.

Detailed Explanation: Classify quadrilaterals

To classify a quadrilateral, look at its sides and angles.

  1. Check that the shape is closed.
  2. Count its straight sides and vertices. It must have exactly 4 of each.
  3. Look for special attributes:
    • Parallelogram: 2 pairs of opposite sides are parallel.
    • Rectangle: 4 right angles.
    • Rhombus: 4 equal sides.
    • Square: 4 equal sides and 4 right angles.
    • Kite: 2 pairs of neighboring sides are equal.

A shape can belong to more than one group. Turning or resizing a shape does not change its classification.

Example

Shape WXYZWXYZ has:

  • 4 straight sides and 4 vertices
  • 4 equal sides
  • 4 right angles
  • 2 pairs of opposite sides that are parallel

Step 1: Identify the broad group.

It is closed and has exactly 4 straight sides, so it is a quadrilateral.

Step 2: Check the side lengths.

All 4 sides are equal, so it is a rhombus.

Step 3: Check the angles.

All 4 angles are right angles, so it is a rectangle.

Step 4: Check both properties together.

A shape with 4 equal sides and 4 right angles is a square.

So, shape WXYZWXYZ is a:

square, rectangle, rhombus, and quadrilateral\boxed{\text{square, rectangle, rhombus, and quadrilateral}}

Learn by doing: Classify quadrilaterals

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Quadrilaterals - Is Shape of a Type (Real World)

      ?