 Properties of Quadrilaterals: Quadrilaterals are closed figures with four sides. There are different types of quadrilaterals known to us. Every closed figure shape with four sides shows varying properties of quadrilaterals that are peculiar to their specific shape. This article shall let you understand the same.

### Suggested Videos        A four-sided polygon along with two dimensions is known as Quadrilateral. A Quadrilateral can be convex or conclave based on their dimensions. If Dimensions are inside the borderline of polygon than it will be termed as a convex quadrilateral. Based on the sides, and angle there are the following six types of convex Quadrilaterals.

• Parallelogram
• Rectangle
• Square
• Rhombus
• Trapezium
• Kite

Learn the Basics of Rectangle and Square here.

But before elaborating the properties of the above quadrilateral we will go through a few common properties of quadrilateral that will be visible in every type of quadrilaterals-

• Every quadrilateral has four sides.
• Every quadrilateral consist of four corners or vertex

Now let us discuss the properties of every quadrilateral separately-

### Properties of Parallelogram

• Opposite sides are equal and parallel to each other.
• Opposite angles are equal.
• The adjacent angles are supplementary.
• Diagonals bisect each other. ### Properties of Rectangle

• Opposite sides are equal.
• All angles in the rectangle are the right angle.
• Diagonals are congruent and bisect each other. ### Properties of Square

• All sides are equal in square.
• Every interior angle will be of 90°.
• Diagonals are perpendicular and bisect each other.

### Properties of Rhombus

• All sides are congruent.
• Diagonals intersect each other and are perpendicular to each other.
• Opposite angles are congruent.
• Adjacent angles are supplementary. ### Properties of Kite

• Two pairs of adjacent size are congruent.
• The angle between unequal sides are equal
• Diagonals intersect each other.
• One diagonal is perpendicular to another.

### Properties of Trapezium

• One pair of opposite side is parallel.
• Diagonals intersect each other in the same ratio.
• Two adjacent angles are supplementary.

After going through the above properties of every quadrilateral it will now be easier for you to differentiate between them. So every quadrilateral is a four-sided figure but still, there is a lot of difference between them depending on the length of sides and the equality of angle. The difference between them is mentioned in their properties, so go through the above properties carefully as you are now able to differentiate between every type of quadrilateral.

## Solved example for you

Question 1: In the adjoining figure, PQRS is a parallelogram. Find x and y in cm Answer: In a parallelogram, we know that the diagonals bisect each other. Therefore,
SO = OQ
This given,16 = x + y
Similarly, PO = OR,
So that 20 = y + 7
We obtain y = 20 – 7 = 13 cm.
Substituting the value of y in the first relation, we get 16 = x + 13. Hence x = 3 cm.

Question 2: What are the properties of quadrilaterals?

Answer: Quadrilaterals are basically closed figures that have four sides. There are different kinds of quadrilaterals that we know of. Every closed figure shape having four sides shows different properties of quadrilaterals which are unique to their particular shape.

Question 3: What are the convex quadrilaterals?

Answer: When we look at quadrilaterals on the basis of their sides, angle, there are six types. They are parallelogram, rectangle, square, rhombus, trapezium and a kite.

Question 4: What are the properties of a trapezium?

Answer: The properties of a trapezium are that one pair of the opposite side is parallel. Further, the diagonals intersect each other in the same ratio. Finally, the two adjacent angles are supplementary.

Question 5: What shape has 4 sides with different lengths?

Answer: A rhombus refers to a four-sided shape that has all sides with equal length. Moreover, the opposite sides are parallel and opposite angles are equal. Further, one other interesting thing is that the diagonals meet in the middle at the right angle. In other words, they bisect each other at right angles.

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