Quadrilateral: Definition, Types, Properties, Examples

A quadrilateral is a polygon with four sides, four vertices, and four angles. It is one of the most basic shapes in geometry and can be classified into various types based on the properties of its sides and angles.

What is a Quadrilateral?

Also Check: Cube

Types of Quadrilaterals

1. Square

2. Rectangle

3. Rhombus

4. Parallelogram

5. Trapezium (or Trapezoid in some regions)

6. Isosceles Trapezium

7. Kite

Also Check: Isosceles Triangle

Properties of Quadrilateral

• All quadrilaterals have four sides.
• All quadrilaterals have four vertices.
• All quadrilaterals have two diagonals.

Square

• All four sides are equal in length: 𝐴𝐵=𝐵𝐶=𝐶𝐷=𝐷𝐴
• All interior angles are right angles: ∠A=∠B=∠C=∠D=90°.
• It has two pairs of parallel sides: 𝐴AB∥DC and AD∥BC.
• The diagonals are equal in length:AC=BD.

Rectangle

• It has two pairs of parallel sides: AB∥DC and AD∥BC.
• All interior angles are 90°: ∠A=∠B=∠C=∠D=90°.
• The opposite sides are equal: AB=DC and AD=BC.
• The diagonals are equal in length: AC=BD, and they bisect each other.

Parallelogram

• The opposite sides are equal: PQ=RT and PR=QT.
• The opposite angles are equal: ∠P=∠T and ∠Q=∠R.

Trapezium

• The parallel sides are called the "bases" of the trapezium: EF and GH.
• The non-parallel sides are the "legs": EG and FH.
• In a special type of trapezium called an isosceles trapezium, the non-parallel sides are equal, and the diagonals are also equal in length.

Also Check: Quadratic Equation

Rhombus

• All four sides are equal: EH=HG=GF=FE.
• The opposite angles are equal: ∠E=∠G and ∠H=∠F.
• The diagonals are perpendicular and bisect each other: EG⊥HF.

Kite

• It has two pairs of equal adjacent sides:  AB=BC and CD=DA.
• One pair of opposite angles (obtuse angles) equals  ∠A=∠C.
• The diagonals are perpendicular: AC⊥BD.
• The longer diagonal bisects the shorter diagonal.
• Each quadrilateral has its own distinct set of properties, but they all share common features, such as having four sides and a total interior angle sum of 360°.

Adjacent Sides of a Quadrilateral

• (AB, BC)
• (BC, CD)
• (CD, DA)
• (DA, AB)

Opposite Sides of a Quadrilateral

• (DA, BC)
• (CD, AB)

Adjacent Angles of a Quadrilateral

• (∠D, ∠A)
• (∠A, ∠B)
• (∠B, ∠C)
• (∠C, ∠D)

Opposite Angles of a Quadrilateral

• (∠A, ∠C)
• (∠B, ∠D)