In this chapter we will discuss basics of quadrilateral and its types.
Important properties of quadrilateral are also discussed in the chapter so make sure you remember it.
What are Quadrilaterals?
Any two dimensional closed shape with 4 sides are known as Quadrilaterals.
Examples of Quadrilateral are:
From the above examples we can note that:
(a) All the figure have four sides
(b) The figures can be of different shapes and sizes
Types of Quadrilateral
Some of the common form of quadrilateral used in geometry are;
(a) Square
(b) Rectangle
(c) Parallelogram
(d) Rhombus
(e) Trapezium
Let us study their property one by one.
Square
Its a 2D figure of four sides in which all sides are equal and each angle measures 90 degree
Important Points for Square
(a) It has 4 sides
(b) Opposite sides are parallel
(c) Each angle is 90 degree
Given above are two examples of square.
(a) Side Length: All sides are equal
(b) Side Orientation : Opposite sides are parallel
(c) Angles: All angles are 90 degree
∠ A = ∠ B = ∠ C = ∠ D = 90 degree
Rectangle
Its a quadrilateral in which Opposite sides are equal and parallel and all angles measure 90 degree
Given above is the rectangle ABCD in which:
(a) Side Length: Opposite sides are equal
AB = CD and AD = BC
(b) Side Orientation : Opposite sides are parallel
(c) Angles: All angles are 90 degree
∠ A = ∠ B = ∠ C = ∠ D = 90 degree
Parallelogram
Parallelogram is a quadrilateral in which Opposite sides are equal and parallel. Also in parallelogram opposite angles are equal.
The above parallelogram has following features;
(a) Side Length: Opposite sides are equal
AB = CD and AD = BC
(b) Side Orientation : Opposite sides are parallel
(c) Angles: Opposite angles are equal
∠ D = ∠B
∠ A = ∠ C
Rhombus
Rhombus is a quadrilateral with following properties;
(a) All sides are equal
(b) Opposite sides are parallel
(c) Opposite angles are equal
Rhombus can also be imagined as tilted square in which sides has been tilted at certain angle.
The quadrilateral looks like a star.
The above rhombus ABCD has following features;
(a) Side Length: All sides are equal
(b) Side Orientation: Opposite sides are parallel
AB parallel to CD
CB parallel to DA
(c) Angles : Opposite angles are equal
∠ D = ∠B
∠ A = ∠ C
Trapezium
Trapezium is a quadrilateral with following properties;
(a) one pair of opposite sides are parallel
(b) the other pairs are non parallel
Given above is figure of trapezium ABCD with following features;
Sides AB & CD are parallel pairs
Sides AD and BC are non parallel pairs
Summary of Quadrilateral
Questions on Quadrilaterals
(01) Identify the below quadrilateral
Solution
The Quadrilateral is a square as:
⟹ Its opposite sides are equal and parallel
⟹ All angles are 90 degree
(02) Identify the below image
Solution
The Quadrilateral is a square as:
⟹ all sides are equal
⟹ all angles are 90 degrees
(03) Identify the below quadrilateral
Solution
The given quadrilateral is a trapezium because:
(a) One pair of opposite sides are parallel ( AD II BC)
(b) Other pairs of sides are not parallel
(04) Given below is the diagram of Rhombus.
The side AB = 6 cm, find the length of side CD
In Rhombus all sides are equal.
Hence, AB = BC = CD = DA = 6 cm
(05) Given below is the figure of parallelogram.
Here ∠B = 75 degree. Find value of ∠D
Solution
We know that in parallelogram opposite angles are equal to each other.
So ∠B = ∠D = 75 degree
(06) Identify the below figure
The above quadrilateral is Rhombus because:
(a) All sides are equal
(b) Opposite sides are parallel
(c) Opposite angles are equal
(07) Below is the image of rectangle
Find the value of all angles
In rectangle all the angles are 90 degree
Hence, ∠A = ∠B = ∠C = ∠D = 90 degree
(08) Two squares ABCD & EFGH are joined to form rectangle PQRS
Its given that AD = 2 cm, find the length of side PQ of the rectangle
Its given that ABCD is a square.
We know that in square, all sides are equal.
Hence, AD = CD = 2 cm
Similarly EFGH is a square with side 2 cm
From the image we can observe that:
⟹ DC + HG = SR
⟹ 2 + 2 = SR
⟹ SR = 4 cm
Since PQSR is a rectangle, the opposite sides are equal
PQ = SR
PQ = 4 cm
Hence, length of side PQ is 4 cm
(09) Identify the below shape
Solution
From the above image you can observe that:
Side AB = CD
Side AD = BC
And all angles are 90 degree
Hence, the above figure is of rectangle