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LL.2 Classify quadrilaterals

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What are quadrilaterals?

Quadrilaterals are four-sided polygons with four angles. The word "quadrilateral" comes from Latin words meaning "four sides."

Examples:
  • A square has four equal sides and four right angles
  • A rectangle has four sides with opposite sides equal and four right angles
  • A kite has two pairs of adjacent sides that are equal in length
Note

All quadrilaterals have four sides, four vertices (corners), and interior angles that add up to 360 degrees.

How are quadrilaterals classified?

Quadrilaterals are classified based on their side lengths, angle measures, and parallel sides.

Classification Steps:
  • Check if all sides are equal
  • Look for parallel sides (sides that never meet)
  • Measure the angles to see if they are right angles (90 degrees)
  • Identify any special properties
Note

Some quadrilaterals belong to multiple categories. For example, a square is also a rectangle and a rhombus.

Square

A square is a quadrilateral with four equal sides and four right angles (90 degrees each).

Properties:
  • All four sides are equal in length
  • All four angles are right angles (90 degrees)
  • Opposite sides are parallel
  • Has two pairs of parallel sides
  • Diagonals are equal in length and bisect each other at right angles
Note

A square is the most regular quadrilateral because it has both equal sides and equal angles.

Rectangle

A rectangle is a quadrilateral with four right angles and opposite sides that are equal and parallel.

Properties:
  • Opposite sides are equal in length
  • All four angles are right angles (90 degrees)
  • Opposite sides are parallel
  • Has two pairs of parallel sides
  • Diagonals are equal in length and bisect each other
Note

Every square is a rectangle, but not every rectangle is a square. A rectangle only needs right angles and parallel opposite sides.

Rhombus

A rhombus is a quadrilateral with all four sides equal in length.

Properties:
  • All four sides are equal in length
  • Opposite angles are equal
  • Opposite sides are parallel
  • Has two pairs of parallel sides
  • Diagonals bisect each other at right angles
Note

Every square is a rhombus, but not every rhombus is a square. A rhombus doesn't need to have right angles.

Parallelogram

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Properties:
  • Opposite sides are equal in length
  • Opposite angles are equal
  • Opposite sides are parallel
  • Has two pairs of parallel sides
  • Diagonals bisect each other
Note

Rectangles, squares, and rhombuses are all special types of parallelograms with additional properties.

Trapezoid

A trapezoid is a quadrilateral with at least one pair of parallel sides.

Properties:
  • Has at least one pair of parallel sides
  • The parallel sides are called bases
  • The non-parallel sides are called legs
  • Angles between bases and legs may vary
Note

Some definitions say a trapezoid has exactly one pair of parallel sides, while others say at least one pair. In your class, follow your teacher's definition.

Kite

A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length.

Properties:
  • Two pairs of adjacent sides are equal
  • One pair of opposite angles are equal
  • Diagonals intersect at right angles
  • One diagonal bisects the other
Note

Kites look like the traditional flying kites. They have no parallel sides unless they are special cases like squares.

Understanding the relationships

Many quadrilaterals are related to each other through shared properties.

Relationship Examples:
  • A square is a special type of rectangle (with equal sides)
  • A square is a special type of rhombus (with right angles)
  • Both rectangles and rhombuses are parallelograms
  • All squares, rectangles, and rhombuses are parallelograms
Note

When classifying quadrilaterals, start with the most specific category first. For example, call a shape with four equal sides and four right angles a "square" rather than just a "rectangle."