Class 8 Revision Notes for CBSE Maths Chapter 3 Understanding Quadrilaterals (Free PDF Download)

Parallelogram: 

A quadrilateral with each pair of opposite sides parallel.

1. Opposite sides are equal. 

2. Opposite angles are equal. 

3. Diagonals bisect one another. 

Rhombus: 

A parallelogram with sides of equal length. 

1. All the properties of a parallelogram. 

2. Diagonals are perpendicular to each other. 

Rectangle: 

A parallelogram with a right angle. 

1. All the properties of a parallelogram. 

2. Each of the angles is a right angle. 

3. Diagonals are equal. 

Square: 

A rectangle with sides of equal length. 

All the properties of a parallelogram, rhombus, and a rectangle. 

Kite: 

A quadrilateral with exactly two pairs of equal consecutive sides.

1. The diagonals are perpendicular to one another.

2. One of the diagonals bisects the other.

3. From figure,

$m\angle B=m\angle D$ but $m\angle A\ne m\angle C$

Trapezium: 

A quadrilateral having exactly one pair of parallel sides. 

Diagonal: 

A simple closed curve is made up of only line segments. 

A line segment connecting two non-consecutive vertices of a polygon is called diagonal.

Convex: 

The measure of each angle is less than ${{180}^{0}}$. 

Concave: 

The measure of at least one angle is more than ${{180}^{0}}$.

Quadrilateral: 

A polygon having four sides. 

Element of quadrilateral: 

(i) Sides: 

Line segments joining the points. 

(ii) Vertices:

Point of intersection of two consecutive sides. 

(iii) Opposite sides:

Two sides of a quadrilateral having no common endpoint. 

(iv) Opposite Angles:

Two angles of a quadrilateral not having a common arm. 

(v) Diagonals:

A line segment is obtained by joining the opposite vertices. 

(vi) Adjacent Angles:

Two angles of a quadrilateral having a common arm. 

(vii) Adjacent Sides:

Two sides of a quadrilateral having a common endpoint.

Download CBSE Class 8 Maths Chapter 3 Notes Free PDF

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About Understanding Quadrilaterals Class 8 Notes

A figure bounded by four line segments such that no three of them are parallel form a quadrilateral.

A quadrilateral has four sides, four vertices, and four angles.

Thus below figure ABCD is a quadrilateral that is bounded by four sides i.e AB, BC, CD, and AD. The four vertices are A, B, C, and D. ∠A, ∠B, ∠C, and ∠D make the four angles of the quadrilateral. And it is written as □ABCD and read as quadrilateral ABCD.

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A line segment drawn from one vertex to the opposite vertex is called the diagonal of the quadrilateral. In the below figure, segment AC and BD are the diagonals of the quadrilateral ABCD.

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Terms Related to Quadrilateral

Opposite SIdes: Two sides of a quadrilateral are opposite sides if the sides have no common vertex. In the above figure side AB and DC; Side AD and BC are the two pairs of opposite sides.

Opposite Angles: Two angles of a quadrilateral are opposite angles if they don’t have any common arm. In the above figure, ∠A and  ∠C;  ∠B and ∠D, are two pairs of opposite angles.

Adjacent Sides: Two Sides of a quadrilateral are said to be adjacent if the sides have a common vertex. In the above figure, Side AB and BC; Side BC and CD; Side CD and DA; Side DA and AB are the four pairs of adjacent sides and are also called consecutive sides.

Adjacent Angles: Two angles of a quadrilateral is said to be adjacent angles if the angles have a common side or an arm. In the above figure  ∠A and  ∠B;  ∠B and ∠C, ∠C and  ∠D;  ∠D and ∠A are the four pairs of adjacent angles also called consecutive angles.

Types of Quadrilateral

There are basically six types of quadrilaterals. They are as follows,

Parallelogram: A quadrilateral that has its opposite sides congruent and parallel to each other is a parallelogram. Its opposite angles are also congruent to each other.

Rectangle: A quadrilateral that has its opposite sides equal and all the angles are at right angles(900) is called a rectangle.

Square: A quadrilateral that has all its four sides equal and opposite sides are parallel, and all the angles at right angles(900), is called a square.

Rhombus: A quadrilateral has all its sides equal and its diagonals bisect each other at 900 is called a rhombus.

Trapezium: A quadrilateral that has only one pair of sides are parallel and the two sides are non-parallel is called a trapezium. The sides may not be equal to each other.

Kite: A quadrilateral that has two pairs of equal adjacent sides and unequal opposite sides is Kite.

Quadrilateral Angles

As we know that a quadrilateral has four angles. The sum of the angles of the quadrilateral is 3600.

The sum of all the angles of the □ABCD ∠A +∠B + ∠C + ∠D = 360°.

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In the case of square and rectangle, the measure of all the angles is 900.

Therefore we have ∠A = ∠B = ∠C = ∠D = 90°.

Angle Sum Property of Quadrilateral Theorem

The sum of the measures of four angles of a quadrilateral is 3600

i.e ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°.

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Benefits of Understanding Quadrilaterals Class 8 Notes By Vedantu 

Understanding Quadrilaterals Class 8 Notes prepared by our experts at Vedantu contain formulae, definitions, diagrams, and quick explanations of the important concepts which make it easier for the school students to grasp the topics easily.

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Conclusion 

In conclusion, the Class 8 Revision Notes for CBSE Maths Chapter 3 - Understanding Quadrilaterals provide a valuable resource for students to revise and reinforce their understanding of the topic. These revision notes, available as a free PDF download, cover the important concepts, properties, and characteristics of quadrilaterals in a concise and organized manner. The revision notes begin by introducing the definition of a quadrilateral and its various types, such as parallelograms, rectangles, squares, rhombuses, and trapeziums. Each type is explained with clear explanations and examples, allowing students to grasp the distinguishing features of each quadrilateral.

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