Plane Figure - Quadrilateral

A quadrilateral is a closed figure formed by the intersection of four line segments.
Quadra means four and lateral means sides.

In the above figure 1, a quadrilateral is formed by the intersection of four line segments AB, BC, CD and DA.
A, B, C and D are four corners of the quadrilateral formed by the intersection of the four straight lines AB, BC, CD and DA.
How do you call the above figure?
Quadrilateral ABCD.
That is how, a quadrilateral is called by naming its four corners prefixed with the word Quadrilateral, just as we would say ‘Triangle ABC’.
A quadrilateral is a four sided closed figure formed in one same plane. No two line segments out of the four AB, BC, CD and AD are collinear, i.e. lie on a same straight line.
Note the following terms in a quadrilateral

  • AB, BC, CD and AD are called the sides of a quadrilateral.
  • The four corners A, B, C and D at which any two line segments intersect are called Vertices of the quadrilateral.
  • At the four verties A, B, C and D, the angles that are formed are called Interior angles of the quadrilateral.
  • Any two sides that have a common vertex are called adjacent sides.
  • Vertices next to each other are termed consecutive vertices such as A and B, B and C, C and D and D and A.
  • Vertices which are not consecutive are called non consecutive vertices.
  • A diagonal is a line segment that joins any two non consecutive vertices.
  • In the above quadrilateral, AC and BD are diagonals.
  • The two diagonals AC and BD meet each other at point O.

O is called the point of intersection of the diagonals of the quadrilateral.

  •  Any side can serve for Base. The Altitude or Height will then be the line drawn perpendicular to the base from the opposite vertex.

In the quadrilateral ABDC below, if CD is base, then straight line AE perpendicular to CD is Height or Altitude.

Various Types of Quadrilaterals:
The following are the several types of quadrilaterals.
1. Irregular Quadrilateral
A quadrilateral in which all sides and angles are unequal is an irregular
quadrilateral.
2. Trapezium

A quadrilateral in which one pair of sides is parallel.
3. Parallelogram

It is a quadrilateral in which

  • opposite sides are parallel and equal.
  • opposite angles are equal in measure
  • diagonals bisect each other.
  • The point of intersection of diagonals is mid point of diagonals.
  • sum of two consecutive angles is 1800

4. Rhombus    

It is a parallelogram in which

  • all sides are equal
  •  diagonals bisect and are perpendicular to each other
  • diagonals are not equal in length

5. Rectangle

A parallelogram in which

  • opposite angles are equal and opposite
  • diagonals bisect each other and are equal in length
  • angles at the four vertices is 900

6. Square

    • A parallelogram in which
    • All sides and angles are equal
    • Diagonals are equal and are perpendicular to each other.