A quadrilateral is a word used in mathematics to describe a shape having four sides and four vertices. The word ‘quadrilateral’ is derived from the Latin word ‘quadri’ meaning variant of four and ‘latus’ meaning side.  

All quadrilaterals also have four angles, a sum of 360 degrees is obtained when all the inner angles of the vertices are added. Some quadrilaterals are convex and some are concave depending on the outer form of the shape. 

Shape having no side or vertices like the circle is not a quadrilateral, but figures occurring inside a circle as quadrilateral is called cyclic quadrilateral or chordal quadrilateral.

Visit Here also to learn more about Pair of Triangles.

Types of Quadrilaterals 

There are six basic shapes that fall in the taxonomy of quadrilaterals: 

Square: 

  1. All sides are equal 
  2. Opposite sides are parallel 
  3. Diagonal lines intersect making 90° 
  4. All angles at vertices are 90° 

Rectangle 

  1. Opposite sides are equal 
  2. Opposite sides are parallel 
  3. All angles at vertices are 90° 
  4. Diagonal lines intersect at the centre 

Rhombus 

  1. All sides are equal 
  2. Opposite sides are parallel 
  3. The diagonal line intersects making 90° 

Parallelogram 

  1. Opposite sides are equal 
  2. Opposite sides are parallel 
  3. Diagonal lines Intersect at the centre 

Trapezium 

  1. One pair of the opposite line is parallel 
  2. It forms a shape of an irregular rectangle 
  3. It has a larger base and a smaller top line 
  4. The angles at the bottom vertices are equal 
  5. The angles at the top vertices are equal 

Simple Quadrilaterals 

The convex and concave quadrilaterals are specified as the simple quadrilaterals. 

Convex Quadrilaterals 

A convex quadrilateral is a four-sided figure or shape in which all inside angles at the vertices add up to 180 degrees or less. Convex quadrilaterals are mostly in irregular shape and have angles of lesser degrees. 

Concave Quadrilaterals 

A concave quadrilateral is a four-sided shape or figure in which all inside angles at the four vertices add up to more than 180 degrees. Concave quadrilaterals mostly have shapes with parallel sides and larger angles. 

Complex Quadrilaterals 

A complex quadrilateral is a self-intersecting four-sided shape. Some other names for complex quadrilateral are butterfly quadrilateral, bow-tie quadrilateral and cross quadrilateral.  

A complex quadrilateral forms a shape with two acute angles and two reflex angles on the inside of the shape. The complex quadrilateral can also be said to make a mirror image of half the shape. Some examples of complex quadrilaterals are crossed trapezoid, antiparallelogram, crossed rectangle, crossed the square. 

Modern Taxonomy of Quadrilaterals 

The Modern Taxonomy of the quadrilaterals discusses the many forms and shapes a quadrilateral can take. Besides the six basic shapes of quadrilaterals, it is further divided into simple and complex quadrilaterals, which are further divided into complex and concave quadrilaterals. 

Another term that is connected with quadrilaterals is ‘Cyclic quadrilateral’ or ‘Chordal quadrilateral’. This word defines a shape having four sides and four vertices but forming a pattern of a circle.   

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