Quadrilaterals: Types and Properties

Types of Quadrilaterals

• Rectangle: A quadrilateral with all angles being right angles (90°) and opposite sides of equal length.
• Square: A rectangle with all sides of equal length.
• Rhombus: A quadrilateral with all sides of equal length, but not necessarily with right angles.
• Trapezoid (or Trapezium): A quadrilateral with at least two pairs of opposite sides that are not parallel.
• Kite: A quadrilateral with two pairs of adjacent sides of equal length, and the angles between them being equal.
• Parallelogram: A quadrilateral with opposite sides being parallel.
• Irregular Quadrilateral: A quadrilateral that does not fit into any of the above categories.

Properties of Quadrilaterals

General Properties

• A quadrilateral has 4 sides, 4 vertices, and 4 angles.
• The sum of the interior angles of a quadrilateral is 360°.

Properties of Specific Types of Quadrilaterals

• Rectangle and Square:
  • Opposite sides are equal and parallel.
  • Diagonals are equal and bisect each other.
• Rhombus:
  • Diagonals are perpendicular and bisect each other.
  • Opposite angles are equal.
• Parallelogram:
  • Opposite sides are parallel and equal.
  • Diagonals bisect each other.
• Trapezoid (or Trapezium):
  • No specific properties, but can have some of the properties of parallelograms or rectangles.

Quadrilaterals

• A quadrilateral is a polygon with 4 sides, 4 vertices, and 4 angles.
• The sum of the interior angles of a quadrilateral is 360°.

Types of Quadrilaterals

• A rectangle is a quadrilateral with all angles being right angles (90°) and opposite sides of equal length.
• A square is a rectangle with all sides of equal length.
• A rhombus is a quadrilateral with all sides of equal length, but not necessarily with right angles.
• A trapezoid (or trapezium) is a quadrilateral with at least two pairs of opposite sides that are not parallel.
• A kite is a quadrilateral with two pairs of adjacent sides of equal length, and the angles between them being equal.
• A parallelogram is a quadrilateral with opposite sides being parallel.
• An irregular quadrilateral is a quadrilateral that does not fit into any of the above categories.

Properties of Quadrilaterals

Rectangle and Square

• Opposite sides are equal and parallel.
• Diagonals are equal and bisect each other.

Rhombus

• Diagonals are perpendicular and bisect each other.
• Opposite angles are equal.

Parallelogram

• Opposite sides are parallel and equal.
• Diagonals bisect each other.

Trapezoid (or Trapezium)

• No specific properties, but can have some of the properties of parallelograms or rectangles.