# CBSE Class 8 Maths Revision Notes Chapter 3

## CBSE Class 8 Mathematics Revision Notes Chapter 3 – Understanding Quadrilaterals

In these Class 8 Mathematics Chapter 3 notes, students will learn about graphs. In addition, with the help of Class 8 Chapter 3 Mathematics notes, students will know how to answer important questions from the chapter on their final examination. The Chapter 3 Mathematics class 8 notes of the CBSE syllabus are carefully taken from NCERT books and will provide students with essential questions that can be asked in the examinations. Moreover, Class 8 Mathematics notes Chapter 3 will be a student’s CBSE revision notes, providing all the necessary information. These notes are based on the CBSE syllabus

## Access Class 8 Mathematics Chapter 3 – ‘Understanding Quadrilaterals’ Notes In 30 Minutes

These notes contain all the topics in the NCERT books concisely. Download the Class 8 Mathematics chapter 3 notes on this page to improve your exam results. Once you go through these notes, you can easily solve CBSE sample papers to test your understanding. These notes also contain CBSE extra questions that will help students test their understanding.

A Quadrilateral is a figure bounded by four line segments where no three lines are parallel.

A quadrilateral consists of four sides, four vertices, and four angles.

Here, figure ABCD is a quadrilateral bounded by four sides, i.e. AB, BC, CD, and AD. The four vertices of the quadrilateral are A, B, C, and D.  The four angles of the quadrilateral are ∠A, ∠B, ∠C, and ∠D, and it is written as □ABCD and read as quadrilateral ABCD.                                      (1)

The diagonal of the quadrilateral refers to a line segment drawn from one vertex to the opposite vertex. For example, In the figure given below, segments AC and BD are the diagonals of the quadrilateral ABCD.

Parallelogram

A Parallelogram refers to a quadrilateral with each pair of opposite sides parallel.

• Opposite sides are equal.
• Opposite angles are equal.
• Diagonals bisect one another.

Rhombus:

It is a parallelogram with sides of equal length. Rhombus is also a type of quadrilateral.

• All the properties of a parallelogram.
• Diagonals are perpendicular to each other.

Rectangle:

A rectangle is a type of parallelogram with a right angle.

• It has all the features of a parallelogram.
• Each angle is a right angle.
• Diagonals are equal.

Square:

• A rectangle with sides of equal length.
• Has every property of a parallelogram, rhombus, and rectangle.

Kite:

A Kite is a quadrilateral having exactly two pairs of equal consecutive sides.

• The diagonals are perpendicular to one another.
• One of the diagonals bisects the other.
• From figure (2),

BC=CD                                                         (2)

Trapezium

A quadrilateral that has a single pair of parallel sides is called a trapezium.

Diagonal:

A diagonal is a simple closed curve that consists of only line segments.

Here, the line segment connects two non-consecutive vertices of a polygon.

Convex:

Here, the measure of each angle is less than 180°.

Concave:

Here, the measure of at least one angle is more than 180°.

It is a polygon that has four sides.

(i) Sides:

Points are joined by line segments.

(ii) Vertices:

Point where the intersection of two consecutive sides happens.

(iii) Opposite sides:

Two sides of a quadrilateral that have no common endpoint.

(iv) Opposite Angles:

Two angles of a quadrilateral that does not have a common arm.

(v) Diagonals:

By joining the opposite vertices, a line segment is obtained.

Two angles of a quadrilateral that has a common arm.

Two sides of a quadrilateral that have a common endpoint.

Opposite Sides: Two sides of a quadrilateral would be opposite if the sides have no common vertex. In the figure given above, sides AB and DC; sides AD and BC are the two pairs of opposite sides.

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

Adjacent Sides: Two sides of a quadrilateral would be adjacent if the sides have a common vertex. In the figure given above, 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 will be called adjacent angles if they have a common side or an arm. In the figure above, ∠A and ∠B; ∠B and ∠C, ∠C and ∠D; ∠D and ∠A are the four pairs of adjacent angles, also called consecutive angles.

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

Parallelogram: A quadrilateral with its opposite sides congruent and parallel to each other. In a parallelogram, the opposite angles are also congruent with one another.

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

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

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

Trapezium: A trapezium is a quadrilateral with only one pair of parallel sides, and the two sides are non-parallel. The sides might not be equal to each other.

Kite:- A Kite is a quadrilateral form with two pairs of equal adjacent sides and unequal opposite sides.

A quadrilateral has four angles. The total of all the angles of the quadrilateral is 360°.

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

The measure of all the angles in a square and rectangle is 90°.

Therefore, ∠A = ∠B = ∠C = ∠D = 90°.

### Angle Sum Property of Quadrilateral Theorem

The total of the measures of four angles of a quadrilateral is 360

i.e ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°.

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### 1. What are the elements of a quadrilateral?

There are various components of the quadrilateral. The segments that link the vertices are called sides. Vertices are the intersections of two adjacent sides. Two quadrilateral angles that have no common arm are called opposite angles. Diagonals are made by joining the vertices on opposing sides of a line segment. Adjacent angles mean two quadrilateral angles that share a common arm.

### 2. What are the different types of quadrilaterals?

Quadrilaterals are divided into six categories. A parallelogram is a form of quadrilateral that has its opposite sides congruent and parallel to each other. A rectangle is a quadrilateral with its opposite sides equal, and all the angles are at right angles(90°). A square is a quadrilateral form with all four sides equal, opposite sides parallel, and all the angles at right angles (90°). A rhombus is a quadrilateral with equal sides, and its diagonals bisect each other at 90°. A trapezium is a form of a quadrilateral with only one pair of parallel sides, and the two sides are non-parallel. Finally, a Kite is a quadrilateral form with two pairs of equal adjacent sides and unequal opposite sides.

### 3. What do you mean by Rectangle?

A quadrilateral with its opposite sides equal and all the angles at right angles(900) is known as a rectangle.

### 4. What do you mean by Trapezium?

A quadrilateral with only one pair of parallel sides, and the two sides are non-parallel, is known as a trapezium. The sides might not be equal to each other.