A quadrilateral is a polygon which has only 4 sides or edges, therefore having 4 corners or vertices. The word ‘quadrilateral’ literally revolves a play of four (quadra) and sides (latus). Quadrilaterals can generally be of regular shapes like squares, trapezoids and kites or irregular and uncharacterised as the one shown below.
Since the figure above has four sides, it is also a quadrilateral. The image below shows the regular types of quadrilaterals.
Types of Quadrilaterals
A quadrilateral where two of its sides are parallel to each other is a trapezoid or a trapezium. If two pairs of sides are parallel to each other, then the quadrilateral is a parallelogram. If the quadrilateral is such that two pairs of sides are parallel to each other, and all sides are equal to each other in length, then the quadrilateral is a rhombus.
Rectangles and squares can also be considered as parallelograms. But they are special types of parallelograms where all internal angles are equal to 90 degree each. For a square, all sides should also be equal in length to each other, like in a rhombus.
A kite is a special type of quadrilateral, where two pairs of adjacent sides are equal in length to each other, as shown in the image illustrated above.
Another way to classify the types of quadrilaterals is as given below.
- concave quadrilaterals
- convex quadrilaterals
- intersecting quadrilaterals
The images of these are as given below.
Properties of Quadrilateral
A quadrilateral is a four-sided polygon. Properties of quadrilateral are:
- Every quadrilateral has 4 vertices and 4 sides enclosing 4 angles.
- The sum of its interior angles is 360 degrees.
- A quadrilateral which has all 4 equal sides and 4 angles as 90 degrees is a square.
- A quadrilateral which has opposite sides equal and all 4 angles as 90 degrees is a rectangle.
- Parallelogram, rhombus, trapezium and kite are some other types of quadrilateral.
Let us consider a quadrilateral ABCD in the figure below:
- AB, BC, CD and DA are the four sides.
- Points A, B, C and D are the four vertices.
- ∠ABC, ∠BCD, ∠CDA and ∠DAC are the four angles.
- AB and CD are the opposite sides.
- ∠A and ∠C are the opposite angles.
- AB and BC are the adjacent sides.
- ∠A and ∠B are the adjacent angles.
Get detailed solutions to the questions of NCERT Books for chapter ‘Quadrilateral‘along with detailed explanation at BYJU’S.