Types Of Quadrilaterals


Before talking about the types of quadrilaterals, let us recall what a quadrilateral is.

A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles. The sum of its interior angles of a quadrilaterl is 360 degrees. We can also derive the sum of interior angle from the formula of polygon i.e. \(\mathbf{(n-2) \times 180}\)..

A quadrilateral, in general, has sides of different lengths and angles of different measures. However, squares, rectangles, etc. are special types of quadrilaterals with some of their sides and angles being equal. In this article, we will discuss the special types of quadrilaterals and their basic properties.

Types of Quadrilaterals

  • Trapezium: It is a quadrilateral with one pair of opposite parallel sides. In the trapezium ABCD, side AB is parallel to side CD.

Trapezium

  • Parallelogram: It is a quadrilateral with two pairs of parallel sides. The opposite sides are parallel and equal in length. The opposite angles are equal in measure. In the parallelogram ABCD, side AB is parallel to side CD and side AD is parallel to side BC.
    Also, the two diagonals formed intersect each other at the midpoints. As in the figure given below, E is the point where both the diagonals meet. So
    Length AE = EC, & Length BE = ED

Parallelogram

  • Rectangle: It is a quadrilateral with all the 4 angles of equal measure, that is, each of them is 90°. Both the pairs of opposite sides are parallel and equal in length.

Rectangle

  • Rhombus: It is a quadrilateral with all the four sides having equal lengths. The Opposite sides of a rhombus are parallel and opposite angles are equal.

Rhombus

  • Square: It is a quadrilateral in which all the sides and angles are equal. Every angle is a right angle (i.e. 90° each). The pairs of opposite sides are parallel to each other.

Square

  • Kite: It is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

Kite

Some pointers about quadrilaterals to be kept in mind are:

  • Square, rectangle and rhombus are types of parallelograms.
  • A square is a rectangle as well as a rhombus.
  • Rectangle and rhombus are not a square.
  • A parallelogram is a trapezium.
  • A trapezium is not a parallelogram.
  • Kite is not a parallelogram.

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Practise This Question

If ABCD is a rhombus, then the value of x is