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Understanding Quadrilaterals Class 8 Questions And Answers provided here. These NCERT Solutions are created by expert team at craeers360 keeping the latest syllabus and pattern of CBSE 2023-23. A geometrical closed shape made by using 4 straight lines and having four connecting points is called Quadrilateral. The sum of the interior angles in a quadrilateral is always 360 degrees. NCERT Solutions for Class 8 Maths chapter 3 Understanding Quadrilaterals are covering the chapter to help you with the answers and conceptual clarity. It carries around 35% of geometry weightage and includes most important types of questions based on concepts of rectangles, squares, rhombus, parallelograms, trapezium, etc.
NCERT solutions for Class 8 Maths discussed all questions and answers of all chapters including chapter 3 understanding quadrilaterals. The subtopics covered under the chapter are polygons, angle sum property, properties of different kinds of quadrilaterals. In this particular chapter, there are 4 exercises consisting of a total of 31 questions. NCERT solutions for Class 8 Maths chapter 3 Understanding Quadrilaterals is covering every question in a comprehensive manner.
Polygons are categorised based on the quantity of sides or vertices they possess, as outlined below:
Angle Sum Property for Quadrilaterals: The sum of all angles of a quadrilateral is 360°.
Sum of the Measures of Exterior Angles of a Polygon: Regardless of the number of sides in a polygon, the total measure of the exterior angles equals 360 degrees.
>> Categories of Quadrilaterals: Quadrilaterals are grouped based on the measurements of their angles and side lengths. The area represents the total space enclosed by the figure, while the perimeter is the complete distance around its boundaries. Here, you'll find descriptions, area calculations, and perimeter formulas for different types of quadrilaterals:
Free download NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals for CBSE Exam.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise: Angle Sum Property
Answer:
As shown in ACD,
As shown in ABC,
( Since, , , ,
)
Hence proved, the sum of the measures of and
amounts to .
What can you say about the sum of the angles ∠1, ∠2, ∠3 and ∠4?
[Note: We denote the angles by ∠1, ∠2, ∠3, etc., and their respective measures by m∠1, m∠2, m∠3, etc.]
The sum of the measures of the four angles of a quadrilateral is___________.
You may arrive at this result in several other ways also.
Answer:
As we know the sum of all four angles of a quadrilateral is .
are four angles of quadrilateral ABCD.
Hence, the sum of these angles is =
Angles ∠1, ∠2, ∠3, ∠4 meet at a point and sum of these angles is = .
Answer:
As we know
Hence, the sum of
Answer:
Draw a line matching points B and D.Line BD divides ABCD in two triangles . and .
Sum of angles of =
Sum of angles of =
Here,
Adding equation 1 and equation 2,
{ and
i.e. = . }
The sum of the interior angles in a quadilateral,
=
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Exercise: 3.1
Q1 (a) Given here are some figures.
Classify each of them on the basis of the following.
(a) Simple curve
Answer:
(a) Simple curve : The curve which does not cross itself and have only one curve.
Some simple curves are
Q1 (b) Given here are some figures.
Classify each of them on the basis of the following.
(b) Simple closed curve
Answer:
Simple closed curve : The simple curves which are closed by line segment or curved line.
Some simple closed curve are
Q1 (c) Given here are some figures.
Classify each of them on the basis of the following.
(c) Polygon
Answer:
A normally closed curve made up of more than 4 line segments is called a polygon.
Some polygons are shown in figures
Q1 (d) Given here are some figures.
Classify each of them on the basis of the following.
(d) Convex polygon
Answer:
(d) Convex polygon :Convex polygon are polygons having all interior angles less than .
Convex polygon = 2.
Q1 (e) Given here are some figures.
Classify each of them on the basis of the following.
(e) Concave polygon
Answer:
(e) Concave polygon : Concave polygon have one or more interior angles greater than .
Concave polygon = 1.
Q2 (a) How many diagonals does each of the following have?
A convex quadrilateral
Answer:
(a) A convex quadrilateral :
There are 2 diagonals in a convex quadrilateral.
Q2 (b) How many diagonals does each of the following have?
A regular hexagon
Answer:
(b) A regular hexagon :
Total number of diagonal a regular hexagon have are 9 .
Q2 (c) How many diagonals does each of the following have?
A triangle
Answer:
(c) A triangle
A triangle does not have any diagonal.
Answer:
The sum of the measures of the angles of a convex quadrilateral is . A convex quadrilateral is made of two triangles and sum of angles of a triangle is . Hence,sum of angles of two triangles is which is also sum of angles of a quadrilateral.
Here,as we can see this quadrilateral has two triangles and the sum of angles of these triangles is = sum of all angles of a quadrilateral.
What can you say about the angle sum of a convex polygon with the number of sides?
(a) 7
Answer:
(a) 7
the sum of angles of a convex polygon
the sum of angle of a convex polygon with 7 sides
the sum of angles of a convex polygon with 7 sides
the sum of angles of a convex polygon with 7 sides
What can you say about the angle sum of a convex polygon with the number of sides?
(b) 8
Answer:
(b) 8
The sum of the angles of a convex polygon
The sum of the angles of a convex polygon with 8 sides
The sum of the angles of a convex polygon with 8 sides
The sum of the angles of a convex polygon with 8 sides
What can you say about the angle sum of a convex polygon with number of sides?
(c) 10
Answer:
(c) 10
angle sum of a convex polygon
angle sum of a convex polygon with 10 sides
angle sum of a convex polygon with 10 sides
angle sum of a convex polygon with 10 sides
What can you say about the angle sum of a convex polygon with number of sides?
(d)
Answer:
(d)
All the angles of a convex polygon added up to
the sum of the angles of a convex polygon having n sides
Q5 (i) What is a regular polygon?
State the name of a regular polygon of 3 sides
Answer:
A regular polygon is a polygon which has equal sides and equal angles.
The name of a regular polygon of 3 sides is an equilateral triangle.
All sides of the equilateral triangle are equal and angles are also equal.
Each angle =
Q5 (ii) What is a regular polygon?
State the name of a regular polygon of 4 sides
Answer:
A regular polygon is a polygon which has equal sides and equal angles.
The name of a regular polygon of 4 sides is square.
Square has all angles of and all sides are equal.
Q5 What is a regular polygon?
State the name of a regular polygon of 6 sides
Answer:
A regular polygon is a polygon which have equal sides and equal angles.
The name of a regular polygon of 6 sides is a hexagon.
All angles of the hexagon are each.
Q6 Find the angle measure in the following figures.
Answer:
The solution for the above-written question is mentioned below,
Sum of angles of a quadrilateral
Q6 Find the angle measure in the following figures.
Answer:
The Solution for the above-written question is mentioned below,
Sum of angles of a quadrilateral
Q6 Find the angle measure in the following figures.
Answer:
This pentagon has all sides and all angles equal.
Sum of all angles of pentagon is
Q6 Find the angle measure in the following figures.
Answer:
(linear pair) (linear pair)
Sum of all angles of pentagon =
Q7 (a) Find
Answer:
(a) Find
The Sum of all angles of triangle is
the unmarked angle of triangle be A.
=
=
Q7 (b) Find
Answer:
Here you will find the detailed solution of the above-written question,
Sum of all angles of quadrilateral =
Let the unmarked angle be A.
=
=
NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals Excercise: Sum of the Measures of the Exterior Angles of a Polygon
Take a regular hexagon Fig 3.10.
Q1 What is the sum of the measures of its exterior angles
Answer:
the sum of all its exterior angles will be equal to .
x,y,z,p,q,r are all exterior angles.
Hence,
Q2 Take a regular hexagon Fig 3.10.
Answer:
It is a hexagon with all sides equal.
All interior angles are also equal.
(linear pairs)
Hence,
because it is a hexagon with all sides and angles equal.
Q3 (i) What is the measure of each? exterior angle
Answer:
It is a hexagon with all sides equal.
All interior angles are also equal.
Sum of all angles of hexagon is .
(linear pairs)
Each exterior angle = = =
Q3 (ii) What is the measure of each? interior angle
Answer:
It is a hexagon with all sides equal.
All interior angles are also equal.
Sum of all angles of the hexagon is .
Q4 (i) Repeat this activity for the cases of a regular octagon
Answer:
(i) a regular octagon: It has all 8 angles equal and sum of all eight angles is 1080. Interior angles are equal so exterior angles are also equal.
Let interior angle be A.
.
All exterior angles be B.
Q4 (ii) Repeat this activity for the cases of a regular 20-gon
Answer:
(ii) a regular 20-gon: It has all 20 angles equal and sum of all eight angles is 3240.Interior angles are equal so exterior angles are also equal.
Let interior angle be A.
.
All exterior angles be B.
Class 8 maths chapter 3 question answer - Exercise: 3.2
Q1 (a) Find in the following figures.
Answer:
Sum of all exterior angles of a polygon is
Q2 (i) Find the measure of each exterior angle of a regular polygon of 9 sides
Answer:
A regular polygon of 9 sides has all sides, interior angles and exterior angles equal.
Sum of exterior angles of a polygon =
Let the interior angle be A.
Sum of exterior angles of 9 sided polygon =
Exterior angles of 9 sided polygon
Hence, the measure of each exterior angle of a regular polygon of 9 sides is
Q2 (ii) Find the measure of each exterior angle of a regular polygon of 15 sides
Answer:
A regular polygon of 15 sides has all sides, interior angles and exterior angles equal.
Sum of exterior angles of a polygon =
Let the interior angle be A.
Sum of exterior angles of 15 sided polygon =
Exterior angles of 15 sided polygon
Hence, the measure of each exterior angle of a regular polygon of 15 sides is
Q3 How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Answer:
The measure of an exterior angle is 24°
A regular polygon has all exterior angles equal.
Sum of exterior angles of a polygon =
Let a number of sides be X.
Sum of exterior angles of a polygon =
Exterior angles of 15 sided polygon
Hence, sided regular polygon have measure of an exterior angle 24°
Q4 How many sides does a regular polygon have if each of its interior angles is 165°?
Answer:
The measure of each interior angle is 165°
So, measure of each exterior angle = 180°-165° = 15°
Regular polygon has all exterior angles equal.
Let number of sides of polygon = n
Sum of Exterior angles of a polygon =
Hence,regular polygon having each of its interior angles is 165° has 24 sides.
Q5 (a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
Answer:
The measure of an exterior angle is 22°
A regular polygon has all exterior angles equal.
Sum of exterior angles of a polygon =
Let the number of sides be X.
Sum of exterior angles of a polygon =
Exterior angles of 15 sided polygon
Hence, the side of a polygon should be an integer but as shown above, the side is not an integer. So,it is not possible to have a regular polygon with the measure of each exterior angle as 22o.
Q5 (b) Can it be an interior angle of a regular polygon? Why?
Answer:
The measure of an interior angle is 22°
A regular polygon has all interior angles equal.
Let the number of sides and number of interior angles be n.
Sum of interior angles of a polygon =
Sum of interior angles of a polygon = =
The number of sides of a polygon should be an integer but since it is not an integer.So, it cannot be a regular polygon with interior angle as 22o
Q6 (a) What is the minimum interior angle possible for a regular polygon? Why?
Answer:
Consider a polygon with the lowest number of sides i.e. 3.
Sum of interior angles of 3 sided polygon =
Interior angles of a regular polygon are equal = A .
Hence,the minimum interior angle possible for a regular polygon is .
Q6 (b) What is the maximum exterior angle possible for a regular polygon?
Answer:
Let there be a polygon with the minimum number of sides i.e. 3.
Exterior angles an equilateral triangle has a maximum measure.
Sum of exterior angles of polygon =
Let the exterior angle be A.
Hence, the maximum exterior angle possible for a regular polygon is .
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Topic: Kinds of Quadrilaterals
You get a trapezium. (Check it!) Which are the parallel sides here? Should the
non-parallel sides be equal?
You can get two more trapeziums using the same set of triangles. Find them out and
discuss their shapes.
Answer:
AB and CD are parallel sides.BC and AD are nonparallel sides. Non-parallel sides need not be equal.
We can get two more trapeziums using the same set of triangles-
and
Fold both the diagonals of the kite. Use the set-square to check if they cut at
right angles. Are the diagonals equal in length? Verify (by paper-folding or measurement) if the diagonals bisect each other. By folding an angle of the kite on its opposite, check for angles of equal measure.
Observe the diagonal folds; do they indicate any diagonal being an angle bisector? Share your findings with others and list them. A summary of these results are given elsewhere in the chapter for your reference. Show that triangle ABC and triangle ADC
are congruent. What do we infer from this?
Answer :
Kite has symmetry along AC diagonal. and are congruent and equal triangles.
Diagonals AC and BD are of different lengths.
Diagonals bisect each other.
The two diagonals AC and BD bisect .
NCERT Solutions for Class 8 Maths 3 Understanding Quadrilaterals Excercise: Elements of Parallelogram
Q1 Take cut-outs of two identical parallelograms, say ABCD and A′B′C′D′ (Fig 3.19).
Here is same as except for the name. Similarly the other corresponding
sides are equal too.
Place over . Do they coincide? What can you now say about the lengths
and ?
Similarly examine the lengths and . What do you find?
You may also arrive at this result by measuring and .
Answer:
Take cut-outs of two identical parallelograms, say ABCD and A′B′C′D′ (Fig 3.19).
Here is same as .
Also, is same as
Place over . They coincide with each other.
The lengths and are equal and parallel lines.
The lengths and are equal and parallel lines.
Property: The opposite sides of a parallelogram are of equal length.
Answer:
Property : The opposite sides of a parallelogram are of equal length.
As we can see in the figure above, the opposite sides of figure are equal.
The figure above is a rectangle which is part of parallelogram.
Hence, the opposite sides of a parallelogram are of equal length.
Property: The opposite angles of a parallelogram are of equal measure.
Answer:
As shown in the above figure opposites angles are equal and are equal to .
Hence,the figure obtained help you to confirm the property: The opposite angles of a parallelogram are of equal measure.
Q4 Take a cut-out of a parallelogram, say,
ABCD (Fig 3.29). Let its diagonals and meet at O.
Find the mid point of by a fold, placing C on A. Is the
mid-point same as O?
Does this show that diagonal bisects the diagonal at the point O? Discuss it
with your friends. Repeat the activity to find where the mid point of could lie.
Answer:
ABCD . Let its diagonals and meet at O.
The mid point of is at point O.Hence, the
mid-point is same as O.
This show that diagonal bisects the diagonal at the point O.
The mid point of is point O.
Class 8 maths chapter 3 NCERT Solutions - exercise: 3.3
Q1 (i) Given a parallelogram ABCD. Complete each statement along with the definition or property used.
......
Answer:
In a parallelogram, opposite sides are equal in lengths.
Hence,
Q1 (ii) Given a parallelogram ABCD. Complete each statement along with the definition or property used.
......
Answer:
In a parallelogram ,opposite angles are equal.
(ii)
Q1 (iii) Given a parallelogram ABCD. Complete each statement along with the definition or property used.
......
Answer:
In a parallelogram, both diagonals bisect each other.
Q1 (iv) Given a parallelogram ABCD. Complete each statement along with the definition or property used.
.....
Answer:
In a parallelogram, adjacent angles are supplementary to each other.
(iv)
Q2 (i) Consider the following parallelograms. Find the values of the unknowns .
Answer:
In a parallelogram, adjacent angles are supplementary to each other.
Opposite angles are equal.
Hence, z =
and y = 100
Q2 (ii) Consider the following parallelograms. Find the values of the unknowns .
Answer:
( Two adjacent angles are supplementary to each other)
x=y= (opposite angles are equal)
z=x= ( corresponding angles are equal)
Q2 (iii) Consider the following parallelograms. Find the values of the unknowns .
Answer:
x= (vertically opposite angles)
(sum of angles of a triangle is )
y=z= (alternate interior angles)
Q2 (iv) Consider the following parallelograms. Find the values of the unknowns .
Answer:
(adjacent angles are supplementary)
y = ( opposite angles are equal)
z= (corresponding angles are equal)
Q2 (v) Consider the following parallelograms. Find the values of the unknowns .
Answer:
y = (opposite angles are equal)
(adjacent angles are supplementary)
x = z = (alternate angles are equal)
Q3 (i) Can a quadrilateral ABCD be a parallelogram if
Answer:
(i)
Opposite angles should be equal and adjacent angles should be supplementary to each other.
are opposite angles.
Hence, a quadrilateral ABCD can be a parallelogram but it is not confirmed.
Q3 (ii) Can a quadrilateral ABCD be a parallelogram if
and ?
Answer:
Opposite sides of a parallelogram are equal in length.
Since, and are opposite sides and have different lengths.
No, it is not a parallelogram.
Q3 (iii) Can a quadrilateral ABCD be a parallelogram if and ?
Answer:
Opposite angles of a parallelogram are equal
Since here and are different.
So, it is not a parallelogram.
Answer:
The above-shown figure shows two opposite angles equal. .
But, it's not a parallelogram because the other two angles are different i.e. .
Answer:
The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2.
Sum of adjacent angles is .
Hence, angles are and .
Let there be a parallelogram ABCD then, and . (Opposite angles are equal).
Answer:
Given: Two adjacent angles of a parallelogram have equal measure = .
( adjacent angles of a parallelogram are supplementary)
and ( Opposite angles of a parallelogram are equal)
Hence,
Answer:
The adjacent figure HOPE is a parallelogram.
(linear pairs)
(opposite angles of a parallelogram are equal)
( adjacent angles are supplementary )
y= (Alternate interior angles are equal)
Q8 (i) The following figures GUNS and RUNS are parallelograms. Find and . (Lengths are in cm)
Answer:
GUNS is a parallelogram, so opposite sides are equal in length
Hence, cm and cm.
Q8 (ii) The following figures GUNS and RUNS are parallelograms. Find and . (Lengths are in cm)
Answer:
Diagonals of a parallelogram intersect each other.
Hence, cm and cm.
Q9 In the above figure both RISK and CLUE are parallelograms. Find the value of .
Answer:
( adjacent angles are supplemantary)
(oppsite angles are equal)
(sum of angles of a triangle is )
Q10 Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.32)
Answer:
Given, = .
A transverse line is intersecting two lines such that the sum of angles on the same side of the transversal line is .
And hence, lines KL and MN are parallel to each other.
Quadrilateral KLMN has a pair of parallel lines so it is a trapezium.
Q12 Find the measure of and if in Fig 3.34.
(If you find , is there more than one method to find ?)
Answer:
Given,
(angles on the same side of transversal)
(angles on the same side of transversal)
Yes, to find there is more than one method.
PQRS is quadrilateral so the sum of all angles is 360
and we know
so put values of and we get a measurement of
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Topic: Squares
Property: The diagonals of a square are perpendicular bisectors of each other.
Answer:
PO = OR ( Square is a type of parallelogram)
By SSS congruency rule, and are congruent triangles.
&
Hence, .
Thus,we can say that the diagonals of a square are perpendicular bisectors of each other
NCERT Solutions for Class 8 Maths 3 Understanding Quadrilaterals Exercise: 3.4
Q1 (a) State whether True or False. All rectangles are squares
Answer:
(a). False, All squares are rectangles but all rectangles cannot be square.
Q1 (b) State whether True or False. All rhombuses are parallelograms
Answer:
True. The opposite sides of the rhombus are parallel and equal.
Q1 (c) State whether True or False. All squares are rhombuses and also rectangles.
Answer:
True. All squares are rhombus because rhombus has opposite sides parallel and equal and same square has.
Also, all squares are rectangles because they have all interior angles as .
Q1 (d) State whether True or False. All squares are not parallelograms.
Answer:
False.
All squares have their opposite sides equal and parallel. Hence, they are parallelograms.
Q1 (e) State whether True or False. All kites are rhombuses.
Answer:
False,
Kites do not have all sides equal so they are not rhombus.
Q1 (f) State whether True or False. All rhombuses are kites.
Answer:
True, all rhombuses are kites because they have two adjacent sides equal.
Q1 (g) State whether True or False. All parallelograms are trapeziums.
Answer:
True, all parallelograms are trapezium because they have a pair of parallel sides.
Q1 (h) State whether True or False. All squares are trapeziums.
Answer:
True, All squares are trapeziums because all squares have pairs of parallel sides.
Q2 (a) Identify all the quadrilaterals that have. four sides of equal length
Answer:
The quadrilateral having four sides of equal length are square and rhombus.
Q2 (b) Identify all the quadrilaterals that have. four right angles
Answer:
All the quadrilaterals that have four right angles are rectangle and square
Q3 (i) Explain how a square is a quadrilateral
Answer:
A square is a quadrilateral because a square has four sides.
Q3 (ii) Explain how a square is a parallelogram
Answer:
A square is a parallelogram because the square has opposite sides parallel to each other.
Q3 (iii) Explain how a square is a rhombus
Answer:
A square is a rhombus because a square has four sides equal.
Q3 (iv) Explain how a square is.a rectangle
Answer:
A square is a rectangle since it has all interior angles of .
Q4 (i) Name the quadrilaterals whose diagonals bisect each other
Answer:
The quadrilaterals whose diagonals bisect each other are square, rectangle, parallelogram and rhombus.
Q4 (ii) Name the quadrilaterals whose diagonals are perpendicular bisectors of each other
Answer:
The quadrilaterals whose diagonals are perpendicular bisectors of each other are rhombus and square.
Q4 (iii) Name the quadrilaterals whose diagonals are equal
Answer:
The quadrilaterals whose diagonals are equal are squares and rectangles.
Q5 Explain why a rectangle is a convex quadrilateral.
Answer:
A rectangle is a convex quadrilateral because it has two diagonals and both lie in the interior of the rectangle.
Answer:
Draw line AD and DC such that and .
and
ABCD is a rectangle as it has opposite sides equal and parallel.
All angles of the rectangle are and a rectangle has two diagonals equal and bisect each other.
Hence, AO = BO = CO = DO
O is equidistant from A,B,C,D.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Topic: Rectangle
Answer:
(1).All the properties of a parallelogram.
(2) Each of the angles is a right angle.
(3) Diagonals are equal
Class 8 understanding quadrilaterals NCERT Solutions - Topic: Square
Q2 A square was defined as a rectangle with all sides equal. Can we define it as
rhombus with equal angles? Explore this idea.
Answer:
Properties of the rectangle are :
(1) All the properties of a parallelogram.
(2) Each of the angles is a right angle.
(3) Diagonals are equal.
A square satisfies all the properties of rectangles so a square can be defined as a rectangle with all sides equal.
Properties of a rhombus are :
(1) All the properties of a parallelogram.
(2) Diagonals are perpendicular to each other.
A square satisfies all the properties of the rhombus so we can define it as
rhombus with equal angles.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Topic: Trapezium
Q3 Can a trapezium have all angles equal? Can it have all sides equal? Explain.
Answer:
Trapezium has two sides parallel and the other two sides are non-parallel. Parallel sides may be equal or unequal but we cannot have a trapezium with all sides and angles equal.
Chapter -1 | |
Chapter -2 | |
Chapter-3 | Understanding Quadrilaterals |
Chapter-4 | |
Chapter-5 | |
Chapter-6 | |
Chapter-7 | |
Chapter-8 | |
Chapter-9 | |
Chapter-10 | |
Chapter-11 | |
Chapter-12 | |
Chapter-13 | |
Chapter-14 | |
Chapter-15 | |
Chapter-16 |
Clarity of Concepts: In this maths chapter 3 class 8 we are ocusing on clarifying the fundamental properties and properties of different types of quadrilaterals.
Real-Life Applications: Explaining how the concepts of quadrilaterals are applied in practical situations and in geometry.
Practice Questions: Additional practice problems to reinforce learning and problem-solving skills. Students can practice class 8 maths ch 3 question answer using the pdf.
How to use NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals?
Keep working hard and happy learning!
Also Check NCERT Books and NCERT Syllabus here:
Constructing a Quadrilateral
are the important topics of this chapter.
There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths.
No, CBSE doesn’t provide NCERT solutions for any class or subject.
Here you will get the detailed NCERT solutions for class 8 by clicking on the link.
NCERT solutions are provided in a very detailed manner which will give the conceptual clarity to the students. Also, students can take help from these solutions when they are not able to solve them on their own.
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Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.
If you are intrigued by the programming world and are interested in developing communications networks then a career as database architect may be a good option for you. Data architect roles and responsibilities include building design models for data communication networks. Wide Area Networks (WANs), local area networks (LANs), and intranets are included in the database networks. It is expected that database architects will have in-depth knowledge of a company's business to develop a network to fulfil the requirements of the organisation. Stay tuned as we look at the larger picture and give you more information on what is db architecture, why you should pursue database architecture, what to expect from such a degree and what your job opportunities will be after graduation. Here, we will be discussing how to become a data architect. Students can visit NIT Trichy, IIT Kharagpur, JMI New Delhi.
Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive.
Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.
Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.
Individuals who opt for a career as a stock analyst examine the company's investments makes decisions and keep track of financial securities. The nature of such investments will differ from one business to the next. Individuals in the stock analyst career use data mining to forecast a company's profits and revenues, advise clients on whether to buy or sell, participate in seminars, and discussing financial matters with executives and evaluate annual reports.
A Researcher is a professional who is responsible for collecting data and information by reviewing the literature and conducting experiments and surveys. He or she uses various methodological processes to provide accurate data and information that is utilised by academicians and other industry professionals. Here, we will discuss what is a researcher, the researcher's salary, types of researchers.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.
Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.
A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.
A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.
Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials.
Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.
A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.
Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.
The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.
An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.
Are you searching for an ‘Anatomist job description’? An Anatomist is a research professional who applies the laws of biological science to determine the ability of bodies of various living organisms including animals and humans to regenerate the damaged or destroyed organs. If you want to know what does an anatomist do, then read the entire article, where we will answer all your questions.
For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.
Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.
Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.
Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.
Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.
A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.
A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.
Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.
An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.
They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.
In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.
In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.
Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.
For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.
Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.
Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.
Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.
Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.
A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack
An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.
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