understanding quadrilaterals class 8 assignment

CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 8 Mathematics Understanding Quadrilaterals Assignments

We have provided below free printable Class 8 Mathematics Understanding Quadrilaterals Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 8 Mathematics Understanding Quadrilaterals . These Assignments for Grade 8 Mathematics Understanding Quadrilaterals cover all important topics which can come in your standard 8 tests and examinations. Free printable Assignments for CBSE Class 8 Mathematics Understanding Quadrilaterals , school and class assignments, and practice test papers have been designed by our highly experienced class 8 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Understanding Quadrilaterals Class 8 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Understanding Quadrilaterals Class 8. Students can click on the links below and download all Pdf Assignments for Mathematics Understanding Quadrilaterals class 8 for free. All latest Kendriya Vidyalaya Class 8 Mathematics Understanding Quadrilaterals Assignments with Answers and test papers are given below.

Mathematics Understanding Quadrilaterals Class 8 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 8 Mathematics Understanding Quadrilaterals . Students and teachers can download and save all free Mathematics Understanding Quadrilaterals assignments in Pdf for grade 8th. Our expert faculty have covered Class 8 important questions and answers for Mathematics Understanding Quadrilaterals as per the latest syllabus for the current academic year. All test papers and question banks for Class 8 Mathematics Understanding Quadrilaterals and CBSE Assignments for Mathematics Understanding Quadrilaterals Class 8 will be really helpful for standard 8th students to prepare for the class tests and school examinations. Class 8th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 8 Mathematics Understanding Quadrilaterals Download in Pdf

Advantages of Class 8 Mathematics Understanding Quadrilaterals Assignments

• As we have the best and largest collection of Mathematics Understanding Quadrilaterals assignments for Grade 8, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics Understanding Quadrilaterals textbooks for Class 8 .
• All Mathematics Understanding Quadrilaterals assignments for Class 8 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 8 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics Understanding Quadrilaterals chapter wise worksheets and assignments for free in Pdf
• Class 8 Mathematics Understanding Quadrilaterals question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 8 Mathematics Understanding Quadrilaterals students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Understanding Quadrilaterals Class 8 which you can download in Pdf

We provide here Standard 8 Mathematics Understanding Quadrilaterals chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics Understanding Quadrilaterals in Grade 8, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Understanding Quadrilaterals Grade 8 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 8 for all subjects. You can download them all and use them offline without the internet.

Related Posts

Class 8 Social Science Civics Assignments

Class 8 Mathematics Factorisation Assignments

Class 8 Kannada Assignments

Talk to our experts

1800-120-456-456

• NCERT Solutions for Class 8 Maths Chapter 3 - Understanding Quadrilaterals
• NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals - Free PDF

Students can easily download the free PDF available of NCERT Solutions for Class 8 Maths chapter 3 understanding quadrilaterals from the website. All questions are discussed by the experts of maths teachers and according to the guidelines of NCERT (CBSE). While answering the exercise questions, students will understand the topic in a more comfortable and better way. We try to keep all the answers exciting and straightforward so that students can easily understand. Other than this, you can also download the NCERT Solutions for Class 8 Science . It will help to improve the syllabus and secure good marks in the examinations. NCERT Solutions for all classes and subjects are also available on Vedantu.

Access NCERT Solutions for Class 8 Mathematics Chapter 3– Understanding Quadrilaterals

Exercise 3.1.

1. Given here are some figures.

Classify each of them on the basis of following.

Simple Curve

Ans: Given: the figures $(1)$to $(8)$

We need to classify the given figures as simple curves.

We know that a curve that does not cross itself is referred to as a simple curve.

Therefore, simple curves are $1,2,5,6,7$.

Simple Closed Curve

We need to classify the given figures as simple closed curves.

We know that a simple closed curve is one that begins and ends at the same point without crossing itself.

Therefore, simple closed curves are $1,2,5,6,7$.

We need to classify the given figures as polygon.

We know that any closed curve consisting of a set of sides joined in such a way that no two segments

cross is known as a polygon.

Therefore, the polygons are $1,2$.

Convex Polygon

We need to classify the given figures as convex polygon.

We know that a closed shape with no vertices pointing inward is called a convex polygon.

Therefore, the convex polygon is $2$.

Concave Polygon

We need to classify the given figures as concave polygon.

We know that a polygon with at least one interior angle greater than 180 degrees is called a concave

Therefore, the concave polygon is $1$.

2. How many diagonals does each of the following have? 

A Convex Quadrilateral

Ans: Given: a convex quadrilateral

We need to find the number of diagonals in the given quadrilateral

We know that a four-sided closed shape with no vertices pointing inward is called a convex quadrilateral.

Consider, a convex quadrilateral

Now, make diagonals

Therefore, a convex quadrilateral has 2 diagonals.

A Regular Hexagon

Ans: Given: A regular hexagon

We need to find the number of diagonals of a regular hexagon.

We know that a regular hexagon is a closed curve with six equal sides.

Consider, a regular hexagon

Therefore, a regular hexagon has $9$ diagonals.

Ans:  Given: A triangle

We need to find the number of diagonals of a triangle.

We know that a triangle is a closed curve having three sides.

Consider, a triangle

Therefore, a triangle does not have any diagonal.

3. What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

Ans: Given: A convex quadrilateral

We need to find the sum of the measures of the angles of a convex quadrilateral. Will this property hold if the quadrilateral is not convex?

Consider, a convex quadrilateral ABCD and then make a diagonal AD.

We know that the sum of angles of a triangle is ${180^ \circ }$.

So, In $\vartriangle {\text{ACD}}$

Sum of angles of $\vartriangle {\text{ACD}}$ is ${180^ \circ }$

Now, In $\vartriangle {\text{ABD}}$ 

Sum of angles of $\vartriangle {\text{ABD}}$ is ${180^ \circ }$.

Therefore, sum of angles of a convex quadrilateral will be sum of angles of $\vartriangle {\text{ACD}}$ and $\vartriangle {\text{ABD}}$

$= {180^ \circ } + {180^ \circ } $

$= {360^ \circ } $ 

Now, consider a concave quadrilateral ABCD, and then make a diagonal AC. The quadrilateral ABCD is made of two triangles, $\vartriangle {\text{ACD}}$ and $\vartriangle {\text{ABC}}$.

Consider, $\vartriangle {\text{ACD}}$

The sum of angles of the triangle are ${180^ \circ }$.

Now, consider $\vartriangle {\text{ABC}}$

The sum of the angles of triangle are ${180^ \circ }$.

Therefore, sum of the angles of quadrilateral ABCD will be

$ = {180^ \circ } + {180^ \circ } $

$   = {360^ \circ } $ 

Thus, we can say that the property hold true for a quadrilateral which is not convex because a quadrilateral can be divided into two triangles.

4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides?

Given: the table

We need to observe table and make a statement about the angle sum of a convex polygon with number of sides.

From table, we can observe that the angle sum of a convex polygon with ${\text{n}}$sides is $({\text{n}} - 2) \times {180^ \circ }.$

Therefore, the angle sum of a convex polygon with $7$ number of sides will be

$   = (7 - 2) \times {180^ \circ } $

$   = 5 \times {180^ \circ } $

$ = {900^ \circ } $ 

Ans: Given: the table

Therefore, the angle sum of a convex polygon with $8$ number of sides will be

$   = (8 - 2) \times {180^ \circ } $

$   = 6 \times {180^ \circ } $

$   = {1080^ \circ } $ 

Therefore, the angle sum of a convex polygon with $10$ number of sides will be

$ = (10 - 2) \times {180^ \circ } $

$   = 8 \times {180^ \circ } $

$   = {1440^ \circ } $ 

From table, we can observe that the angle sum of a convex polygon with ${\text{n}}$sides will be

$ = ({\text{n}} - 2) \times {180^ \circ }$

5. What is a regular polygon? State the name of a regular polygon of 

Given: $3$ sides

We need to write the statement of a regular polygon and then state the name of the regular polygon with given number of sides.

A regular polygon is a polygon having all angles equal and all sides equal.

We know that a polygon with three equal sides and each ${60^ \circ }$ angle is a triangle.

So, it will be an equilateral triangle. The diagram will be

Ans: Given: $4$ sides

We know that a polygon with four equal sides and each ${90^ \circ }$ angle is called a square.

So, the diagram will be

Ans: Given: $6$ sides

We know that a polygon with six equal sides and each ${120^ \circ }$ angle is called a regular hexagon.

6.  Find the angle measure ${\text{'x'}}$in the following figures.

Given: A quadrilateral with angles ${50^ \circ },{130^ \circ },{120^ \circ },{\text{x}}$

We need to find the value of ${\text{x}}{\text{.}}$

We know that the sum of all interior angles of a quadrilateral is ${360^ \circ }.$

${50^ \circ } + {130^ \circ } + {120^ \circ }{\text{ + x}} = {360^ \circ } $

 $  \Rightarrow {300^ \circ } + {\text{x}} = {360^ \circ } $

 $  \Rightarrow {\text{x}} = {360^ \circ } - {300^ \circ } $

 $  \Rightarrow {\text{x}} = {60^ \circ } $ 

Given: A quadrilateral with angles ${70^ \circ },{60^ \circ },{\text{x}}$

From given figure, 

$  {90^ \circ } + y = {180^ \circ } $

 $  \Rightarrow y = {180^ \circ } - {90^ \circ } $

 $  \Rightarrow y = {90^ \circ } $ 

Now, the quadrilateral has angles, ${70^ \circ },{60^ \circ },{90^ \circ }{\text{,x}}$

We know that sum of all interior angles of a quadrilateral is ${360^ \circ }.$

Thus, 

$  {70^ \circ } + {60^ \circ } + {90^ \circ }{\text{ + x}} = {360^ \circ } $

$   \Rightarrow {220^ \circ } + {\text{x}} = {360^ \circ } $

 $  \Rightarrow {\text{x}} = {360^ \circ } - {220^ \circ } $

$   \Rightarrow {\text{x}} = {140^ \circ } $ 

Ans: We need to find the value of ${\text{x}}{\text{.}}$

From given figure,

$  {70^ \circ } + {\text{a}} = {180^ \circ } $

 $ \Rightarrow {\text{a}} = {180^ \circ } - {70^ \circ } $

$   \Rightarrow {\text{a}} = {110^ \circ } $ 

$  {60^ \circ } + {\text{b}} = {180^ \circ } $

$   \Rightarrow {\text{b}} = {180^ \circ } - {60^ \circ } $

 $  \Rightarrow {\text{b}} = {120^ \circ } $ 

Therefore, the angles of the pentagon are ${30^ \circ }{\text{,x,}}{110^ \circ },{120^ \circ }{\text{,x}}$

We know that the sum of all interior angles of a pentagon is ${540^ \circ }.$

  ${30^ \circ } + {\text{x}} + {110^ \circ } + {120^ \circ } + {\text{x}} = {540^ \circ } $

  $ \Rightarrow {260^ \circ } + 2{\text{x}} = {540^ \circ } $

  $ \Rightarrow 2{\text{x}} = {540^ \circ } - {260^ \circ } $

 $  \Rightarrow 2{\text{x}} = {280^ \circ } $

  $ \Rightarrow {\text{x}} = \dfrac{{{{280}^ \circ }}}{2} $

 $  \Rightarrow {\text{x}} = {140^ \circ } $ 

Ans: Given: a regular pentagon with angle ${\text{x}}{\text{.}}$

$ 5{\text{x}} = {540^ \circ } $

 $  \Rightarrow {\text{x}} = \dfrac{{{{540}^ \circ }}}{5} $

$   \Rightarrow {\text{x}} = {108^ \circ } $ 

Find ${\text{x}} + {\text{y}} + {\text{z}}$

Given: 

We need to find the value of ${\text{x}} + {\text{y}} + {\text{z}}$.

Property Used:

A linear pair can be defined as two adjacent angles that add up to ${180^ \circ },$ or two angles that combine to form a line or right angle.

Exterior angle theorem: If a polygon is convex, the total of the exterior angle measures, one at each vertex, equals${360^ \circ }$.

Using Linear pair,

$  {\text{z}} + {30^ \circ } = {180^ \circ } $

$   \Rightarrow {\text{z}} = {180^ \circ } - {30^ \circ } $

 $  \Rightarrow {\text{z}} = {150^ \circ } $ 

Again, using Linear pair

$  {\text{x}} + {90^ \circ } = {180^ \circ } $

 $  \Rightarrow {\text{x}} = {180^ \circ } - {90^ \circ } $

$   \Rightarrow {\text{x}} = {90^ \circ } $ 

Using Exterior Angle Theorem,

$  {\text{y}} = {90^ \circ } + {30^ \circ } $

$   \Rightarrow {\text{y}} = {120^ \circ } $ 

$  {\text{x}} + {\text{y}} + {\text{z}} = {90^ \circ } + {120^ \circ } + {150^ \circ } $

Find ${\text{x}} + {\text{y}} + {\text{z}} + {\text{w}}$

We need to find the measure of ${\text{x + y + z + w}}$.

Sum of all the interior angles of a quadrilateral is ${360^ \circ }$.

$  {\text{a}} + {60^ \circ } + {80^ \circ } + {120^ \circ } = {360^ \circ } $

$   \Rightarrow {\text{a}} + {260^ \circ } = {360^ \circ } $

$   \Rightarrow {\text{a}} = {360^ \circ } - {260^ \circ } $

$   \Rightarrow {\text{a}} = {100^ \circ } $ 

$  {\text{a}} + {\text{w}} = {180^ \circ } $

 $  \Rightarrow {100^ \circ } + {\text{w}} = {180^ \circ } $

 $  \Rightarrow {\text{w}} = {180^ \circ } - {100^ \circ } $

$   \Rightarrow {\text{w}} = {80^ \circ } $ 

$  {\text{x}} + {120^ \circ } = {180^ \circ } $

$   \Rightarrow {\text{x}} = {180^ \circ } - {120^ \circ } $

$   \Rightarrow {\text{x}} = {60^ \circ } $ 

$  {\text{y}} + {80^ \circ } = {180^ \circ } $

$   \Rightarrow {\text{y}} = {180^ \circ } - {80^ \circ } $

 $  \Rightarrow {\text{y}} = {100^ \circ } $ 

$  {\text{z}} + {60^ \circ } = {180^ \circ } $

 $  \Rightarrow {\text{z}} = {180^ \circ } - {60^ \circ } $

  $ \Rightarrow {\text{z}} = {120^ \circ } $ 

$  {\text{x}} + {\text{y}} + {\text{z}} + {\text{w}} = {60^ \circ } + {100^ \circ } + {120^ \circ } + {80^ \circ } $

Exercise-3.2

1. Find ${\text{x}}$in the following figures.

We know that the sum of all exterior angles of a polygon is ${360^ \circ }.$

$  {\text{x}} + {125^ \circ } + {125^ \circ } = {360^ \circ } $

$   \Rightarrow {\text{x}} + {250^ \circ } = {360^ \circ } $

$   \Rightarrow {\text{x}} = {360^ \circ } - {250^ \circ } $

$   \Rightarrow {\text{x}} = {110^ \circ } $ 

$  {\text{x}} + {90^ \circ } + {60^ \circ } + {90^ \circ } + {70^ \circ } = {360^ \circ } $

$  \Rightarrow {\text{x}} + {310^ \circ } = {360^ \circ } $

$   \Rightarrow {\text{x}} = {360^ \circ } - {310^ \circ } $

 $  \Rightarrow {\text{x}} = {50^ \circ } $ 

2. Find the measure of each exterior angle of a regular polygon of 

Given: a regular polygon with $9$ sides

We need to find the measure of each exterior angle of the given polygon.

We know that all the exterior angles of a regular polygon are equal.

The sum of all exterior angle of a polygon is ${360^ \circ }$.

Formula Used: ${\text{Exterior}}\;{\text{angle}} = \dfrac{{{{360}^ \circ }}}{{{\text{Number}}\;{\text{of}}\;{\text{sides}}}}$

Sum of all angles of given regular polygon $ = {360^ \circ }$

Number of sides $ = 9$

Therefore, measure of each exterior angle will be

$   = \dfrac{{{{360}^ \circ }}}{9} $

 $  = {40^ \circ } $ 

Given: a regular polygon with $15$ sides

Number of sides $ = 15$

$   = \dfrac{{{{360}^ \circ }}}{{15}} $

$ = {24^ \circ } $ 

3. How many sides does a regular polygon have if the measure of an exterior angle is ${24^ \circ }$?

Ans: Given: A regular polygon with each exterior angle ${24^ \circ }$

We need to find the number of sides of given polygon.

We know that sum of all exterior angle of a polygon is ${360^ \circ }$.

Formula Used: ${\text{Number}}\;{\text{of}}\;{\text{sides}} = \dfrac{{{{360}^ \circ }}}{{{\text{Exterior}}\;{\text{angle}}}}$

Each angle measure $ = {24^ \circ }$

Therefore, number of sides of given polygon will be

$   = \dfrac{{{{360}^ \circ }}}{{{{24}^ \circ }}} $

 $  = 15 $ 

4. How many sides does a regular polygon have if each of its interior angles is ${165^ \circ }$?

Ans: Given: A regular polygon with each interior angle ${165^ \circ }$

We need to find the sides of the given regular polygon.

${\text{Exterior}}\;{\text{angle}} = {180^ \circ } - {\text{Interior}}\;{\text{angle}}$

Each interior angle $ = {165^ \circ }$

So, measure of each exterior angle will be

$   = {180^ \circ } - {165^ \circ } $

$   = {15^ \circ } $ 

Therefore, number of sides of polygon will be

$   = \dfrac{{{{360}^ \circ }}}{{{{15}^ \circ }}} $

$   = 24 $ 

Is it possible to have a regular polygon with measure of each exterior angle as ${22^ \circ }$?

Given: A regular polygon with each exterior angle ${22^ \circ }$

We need to find if it is possible to have a regular polygon with given angle measure.

We know that sum of all exterior angle of a polygon is ${360^ \circ }$. The polygon will be possible if ${360^ \circ }$ is a perfect multiple of exterior angle.

$\dfrac{{{{360}^ \circ }}}{{{{22}^ \circ }}}$ does not give a perfect quotient. 

Thus, ${360^ \circ }$ is not a perfect multiple of exterior angle. So, the polygon will not be possible.

Can it be an interior angle of a regular polygon? Why?

Ans: Given: Interior angle of a regular polygon $ = {22^ \circ }$

We need to state if it can be the interior angle of a regular polygon.

And, ${\text{Exterior}}\;{\text{angle}} = {180^ \circ } - {\text{Interior}}\;{\text{angle}}$

Thus, Exterior angle will be

$   = {180^ \circ } - {22^ \circ } $

 $  = {158^ \circ } $ 

$\dfrac{{{{158}^ \circ }}}{{{{22}^ \circ }}}$ does not give a perfect quotient. 

Thus, ${158^ \circ }$ is not a perfect multiple of exterior angle. So, the polygon will not be possible.

What is the minimum interior angle possible for a regular polygon?

Ans:   Given: A regular polygon

We need to find the minimum interior angle possible for a regular polygon.

A polygon with minimum number of sides is an equilateral triangle.

So, number of sides $ = 3$

${\text{Exterior}}\;{\text{angle}} = \dfrac{{{{360}^ \circ }}}{{{\text{Number}}\;{\text{of}}\;{\text{sides}}}}$

Thus, Maximum Exterior angle will be

$   = \dfrac{{{{360}^ \circ }}}{3} $

$   = {120^ \circ } $ 

We know, ${\text{Interior}}\;{\text{angle}} = {180^ \circ } - {\text{Exterior}}\;{\text{angle}}$

Therefore, minimum interior angle will be

$   = {180^ \circ } - {120^ \circ } $

$   = {60^ \circ } $ 

What is the maximum exterior angel possible for a regular polygon?

Ans: Given: A regular polygon

We need to find the maximum exterior angle possible for a regular polygon.

Therefore, Maximum Exterior angle possible will be

$ = {120^ \circ } $

 Exercise 3.3

1. Given a parallelogram ABCD. Complete each statement along with the definition or property used.

$\;{\text{AD}}$ = $...$

Given: A parallelogram ${\text{ABCD}}$ 

We need to complete each statement along with the definition or property used.

We know that opposite sides of a parallelogram are equal.

Hence, ${\text{AD}}$ = ${\text{BC}}$ 

$\;\angle {\text{DCB }} = $ $...$

Given: A parallelogram ${\text{ABCD}}$.

${\text{ABCD}}$ is a parallelogram, and we know that opposite angles of a parallelogram are equal.

Hence, $\angle {\text{DCB   =  }}\angle {\text{DAB}}$

${\text{OC}} = ...$ 

${\text{ABCD}}$ is a parallelogram, and we know that diagonals of parallelogram bisect each other.

Hence, ${\text{OC  =  OA}}$

$m\angle DAB\; + \;m\angle CDA\; = \;...$

Given : A parallelogram ${\text{ABCD}}$.

${\text{ABCD}}$ is a parallelogram, and we know that adjacent angles of a parallelogram are supplementary to each other.

Hence, $m\angle DAB\; + \;m\angle CDA\; = \;180^\circ $

 2. Consider the following parallelograms. Find the values of the unknowns x, y, z.

Given: A parallelogram ${\text{ABCD}}$

We need to find the unknowns ${\text{x,y,z}}$

The adjacent angles of a parallelogram are supplementary.

Therefore, ${\text{x} + 100^\circ  = 180^\circ }$

${\text{x} = 80^\circ }$ 

Also, the opposite angles of a parallelogram are equal.

Hence, ${\text{z}} = {\text{x}} = 80^\circ $ and ${\text{y}} = 100^\circ $

Given: A parallelogram.

We need to find the values of ${\text{x,y,z}}$

The adjacent pairs of a parallelogram are supplementary.

Hence, $50^\circ  + {\text{y}} = 180^\circ $

${\text{y}} = 130^\circ $

Also, ${\text{x}} = {\text{y}} = 130^\circ $(opposite angles of a parallelogram are equal)

And, ${\text{z}} = {\text{x}} = 130^\circ $ (corresponding angles)

(iii)  

Given: A parallelogram 

${\text{x}} = 90^\circ $(Vertically opposite angles)

Also, by angle sum property of triangles

${\text{x}} + {\text{y}} + 30^\circ  = 180^\circ $

${\text{y}} = 60^\circ $

Also,${\text{z}} = {\text{y}} = 60^\circ $(alternate interior angles)

Given: A parallelogram

Corresponding angles between two parallel lines are equal.

Hence, ${\text{z}} = 80^\circ $ Also,${\text{y}} = 80^\circ $ (opposite angles of parallelogram are equal)

In a parallelogram, adjacent angles are supplementary

Hence,${\text{x}} + {\text{y}} = 180^\circ $

$  {\text{x}} = 180^\circ  - 80^\circ  $

$  {\text{x}} = 100^\circ  $ 

As the opposite angles of a parallelogram are equal, therefore,${\text{y}} = 112^\circ $ 

Also, by using angle sum property of triangles

$  {\text{x}} + {\text{y}} + 40^\circ  = 180^\circ  $

$  {\text{x}} + 152^\circ  = 180^\circ  $

$  {\text{x}} = 28^\circ  $ 

And ${\text{z}} = {\text{x}} = 28^\circ $(alternate interior angles)

3. Can a quadrilateral ${\text{ABCD}}$be a parallelogram if 

(i) $\angle {\text{D}}\;{\text{ + }}\angle {\text{B}} = 180^\circ ?$

Given: A quadrilateral ${\text{ABCD}}$

We need to find whether the given quadrilateral is a parallelogram.

For the given condition, quadrilateral ${\text{ABCD}}$ may or may not be a parallelogram.

For a quadrilateral to be parallelogram, the sum of measures of adjacent angles should be $180^\circ $ and the opposite angles should be of same measures.

(ii) ${\text{AB}} = {\text{DC}} = 8\;{\text{cm}},\;{\text{AD}} = 4\;{\text{cm}}\;$and ${\text{BC}} = 4.4\;{\text{cm}}$

As, the opposite sides ${\text{AD}}$and ${\text{BC}}$are of different lengths, hence the given quadrilateral is not a parallelogram.

(iii) $\angle {\text{A}} = 70^\circ $and $\angle {\text{C}} = 65^\circ $

As, the opposite angles have different measures, hence, the given quadrilateral is a parallelogram.

4. Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

Given: A quadrilateral.

We need to draw a rough figure of a quadrilateral that is not a paralleloghram but has exactly two opposite angles of equal measure.

A kite is a figure which has two of its interior angles, $\angle {\text{B}}$and $\angle {\text{D}}$of same measures. But the quadrilateral ${\text{ABCD}}$is not a parallelogram as the measures of the remaining pair of opposite angles are not equal.

5. The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.

Ans: Given: A parallelogram with adjacent angles in the ratio $3:2$

We need to find the measure of each of the angles of the parallelogram.

Let the angles be $\angle {\text{A}} = 3{\text{x}}$and $\angle {\text{B}} = 2{\text{x}}$

As the sum of measures of adjacent angles is $180^\circ $ for a parallelogram.

$  \angle {\text{A}} + \angle {\text{B}} = 180^\circ  $

 $ 3{\text{x}} + 2{\text{x}} = 180^\circ  $

 $ 5{\text{x}} = 180^\circ  $

 $ {\text{x}} = 36^\circ  $ 

$~\angle A=$ $\angle {\text{C}}$ $= 3{\text{x}} = 108^\circ$and $~\angle B=$ $\angle {\text{D}}$ $= 2{\text{x}} = 72^\circ$(Opposite angles of a parallelogram are equal).

Hence, the angles of a parallelogram are $108^\circ ,72^\circ ,108^\circ $and $72^\circ $.

6. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Given: A parallelogram with two equal adjacent angles.

The sum of adjacent angles of a parallelogram are supplementary.

$  \angle {\text{A}} + \;\angle {\text{B}} = 180^\circ  $

$  2\angle {\text{A}}\;{\text{ =  180}}^\circ  $

$  \angle {\text{A}}\;{\text{ = }}\;{\text{90}}^\circ  $

$  \angle {\text{B}}\;{\text{ = }}\angle {\text{A}}\;{\text{ = }}\;{\text{90}}^\circ  $

Also, opposite angles of a parallelogram are equal

$  \angle {\text{C}} = \angle {\text{A}} = 90^\circ  $

$  \angle {\text{D}} = \angle {\text{B}} = 90^\circ  $ 

Hence, each angle of the parallelogram measures $90^\circ $.

7. The adjacent figure ${\text{HOPE}}$is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

Given: A parallelogram ${\text{HOPE}}$.

We need to find the measures of angles ${\text{x,y,z}}$and also state the properties used to find these angles.

$\angle {\text{y}} = 40^\circ $(Alternate interior angles)

And $\angle {\text{z}} + 40^\circ  = 70^\circ $(corresponding angles are equal)

$\angle {\text{z}} = 30^\circ $

Also, ${\text{x}} + {\text{z}} + 40^\circ  = 180^\circ $(adjacent pair of angles)

${\text{x}} = 110^\circ $

8. The following figures ${\text{GUNS}}$and ${\text{RUNS}}$are parallelograms. Find ${\text{x}}$and${\text{y}}$. (Lengths are in cm).

Given: Parallelogram ${\text{GUNS}}$.

We need to find the measures of ${\text{x}}$and ${\text{y}}$.

${\text{GU = SN}}$(Opposite sides of a parallelogram are equal).

$  3{\text{y }} - {\text{ }}1{\text{ }} = {\text{ }}26{\text{ }} $

$  3{\text{y }} = {\text{ }}27{\text{ }} $

$  {\text{y }} = {\text{ }}9{\text{ }} $ 

Also,${\text{SG = NU}}$

Therefore, 

$  3{\text{x}} = 18 $

$  {\text{x}} = 3 $ 

Given: Parallelogram ${\text{RUNS}}$

We need to find the value of ${\text{x}}$and ${\text{y}}{\text{.}}$

The diagonals of a parallelogram bisect each other, therefore, 

$  {\text{y }} + {\text{ }}7{\text{ }} = {\text{ }}20{\text{ }} $

$  {\text{y }} = {\text{ }}13 $

 $ {\text{x }} + {\text{ y }} = {\text{ }}16 $

$  {\text{x }} + {\text{ }}13{\text{ }} = {\text{ }}16 $

 $ {\text{x }} = {\text{ }}3{\text{ }} $ 

9. In the above figure both ${\text{RISK}}$and ${\text{CLUE}}$are parallelograms. Find the value of ${\text{x}}{\text{.}}$

Given: Parallelograms ${\text{RISK}}$and ${\text{CLUE}}$

As we know that the adjacent angles of a parallelogram are supplementary, therefore, 

In parallelogram ${\text{RISK}}$

$  \angle {\text{RKS  + }}\angle {\text{ISK}} = 180^\circ  $

 $ 120^\circ  + \angle {\text{ISK}} = 180^\circ  $ 

As the opposite angles of a parallelogram are equal, therefore,

In parallelogram ${\text{CLUE}}$,

$\angle {\text{ULC}} = \angle {\text{CEU}} = 70^\circ $

Also, the sum of all the interior angles of a triangle is $180^\circ $

$  {\text{x }} + {\text{ }}60^\circ {\text{ }} + {\text{ }}70^\circ {\text{ }} = {\text{ }}180^\circ  $

$  {\text{x }} = {\text{ }}50^\circ  $ 

10. Explain how this figure is a trapezium. Which of its two sides are parallel?

We need to explain how the given figure is a trapezium and find its two sides that are parallel.

If a transversal line intersects two specified lines in such a way that the sum of the angles on the same side of the transversal equals $180^\circ $, the two lines will be parallel to each other.

Here, $\angle {\text{NML}} = \angle {\text{MLK}} = 180^\circ $

Hence, ${\text{NM}}||{\text{LK}}$

Hence, the given figure is a trapezium.

11. Find ${\text{m}}\angle {\text{C}}$in the following figure if ${\text{AB}}\parallel {\text{CD}}$${\text{AB}}\parallel {\text{CD}}$.

Given: ${\text{AB}}\parallel {\text{CD}}$ and quadrilateral

We need to find the measure of $\angle {\text{C}}$

$\angle {\text{B}} + \angle {\text{C}} = 180^\circ $(Angles on the same side of transversal).

$  120^\circ  + \angle {\text{C}} = 180^\circ  $

$  \angle {\text{C}} = 60^\circ  $ 

12. Find the measure of $\angle {\text{P}}$and$\angle {\text{S}}$, if ${\text{SP}}\parallel {\text{RQ}}$in the following figure. (If you find${\text{m}}\angle {\text{R}}$, is there more than one method to find${\text{m}}\angle {\text{P}}$?)

Given: ${\text{SP}}\parallel {\text{RQ}}$and 

We need to find the measure of $\angle {\text{P}}$and $\angle {\text{S}}$.

The sum of angles on the same side of transversal is $180^\circ .$

$\angle {\text{P}} + \angle {\text{Q}} = 180^\circ $

$  \angle {\text{P}} + 130^\circ  = 180^\circ  $

$  \angle {\text{P}} = 50^\circ  

 $\angle {\text{R }} + {\text{ }}\angle {\text{S }} = {\text{ }}180^\circ {\text{ }} $

$  {\text{ }}90^\circ {\text{ }} + {\text{ }}\angle {\text{S }} = {\text{ }}180^\circ  $

  ${\text{ }}\angle {\text{S }} = {\text{ }}90^\circ {\text{ }} $ 

Yes, we can find the measure of ${\text{m}}\angle {\text{P}}$ by using one more method.

In the question,${\text{m}}\angle {\text{R}}$and ${\text{m}}\angle {\text{Q}}$are given. After finding ${\text{m}}\angle {\text{S}}$ we can find ${\text{m}}\angle {\text{P}}$ by using angle sum property.

Different Types of Polygons, Their Sides, and Angle Sum

Polygons are closed figures having at least or more than three sides. They are made of line segments only. Polygons are classified according to the number of sides they have. Some of the most common polygons and their properties are given in the table below.

Understanding Quadrilaterals Class 8

According to geometry, a quadrilateral is a covered, two-dimensional shape that has four straight sides. The polygon has four vertices or corners. Quadrilaterals will typically imply approved forms with four sides like rectangle, square, Trapezoid, kite, or uneven and uncharacterized. From the polygon formula, we can also derive the Sum of interior angles, i.e. (n - 2) × 180, where n stands for the polygon's number of sides. However, squares, rectangles, etc., are particular types of quadrilaterals with some of their sides and equal angles.

Different Types of Quadrilaterals

There are five types of quadrilaterals based on their shape:

Parallelogram

A rectangle is a kind of quadrilateral having four right angles. Hence, every angle in a rectangle is equal (360°/4 = 90°). Moreover, the opposite planes of a rectangle are parallel and similar. Diagonals bisect each other. Letting the length of the rectangle L and breadth B then,

Area of a Rectangle = Length(L) × Breadth(B).

Perimeter = 2 × (L + B).

Properties:

Every angle of a rectangle are 90°.

Opposite sides are equal and Parallel.

Diagonals of a rectangle bisect each other.

Square is another quadrilateral having four equal sides and angles. It's also a normal quadrilateral as both its sides and angles are equal. Accurately like a rectangle, a square has four angles of 90 degrees each. We can also call it a rectangle whose two adjacent sides are equal. Letting the side of a square 'a' then,

Area = a × a = a².

Perimeter = 2 × (a + a) = 4a.

All the angles are 90°.

Each and every side is parallel and also equal to each other.

Diagonals bisect each other perpendicularly.

A parallelogram is a simple quadrilateral whose opposite sides are parallel, as we can understand by the name itself. Thus, it consists of two pairs of parallel sides. Besides, the opposite angles in a parallelogram are alike, and its diagonals divide each other.

Opposite angles are equal.

Opposite sides are equal and parallel.

Diagonals bisect each other.

The summation of any two adjacent angles is 180 degrees.

A rhombus is also a quadrilateral whose all four sides are identical in length and opposite sides parallel. However, the angles are not similar to 90°. A rhombus with right angles would match a square. We often call rhombus a diamond' as it looks similar to the diamond suit in playing cards. Letting the side of a rhombus is 'a' then, the perimeter = 4a.

Considering the length of two diagonals of the rhombus are d1 and d2, then the rhombus area = ½ × d1 × d2.

All planes are equal, and opposite planes are parallel.

The diagonals bisect each other at 90°.

A trapezium is also a quadrilateral having one parallel side pair. The parallel sides are known as 'bases,' and the rest are known as 'legs' or lateral sides. Letting the height of a trapezium 'h' then:

Perimeter = Sum of lengths of all the sides = AB + BC + CD + DA.

Area = ½ × (Sum of lengths of parallel sides) × h = ½ × (AB + CD) × h.

A trapezium is another type of quadrilateral in which it follows a single property where only one pair of opposite sides of trapezium should be parallel to each other.

Kite: A Special Quadrilateral

Kite is a quadrilateral that has the following properties.

It has two pairs of consecutive sides that are equal in size.

Diagonals intersect each other at 90°, therefore the diagonals of a kite are perpendicular to each other.

When diagonals intersect each other, only one of them will be bisected.

NCERT Solutions for Class 8 Maths - Chapterwise Solutions

Chapter 1 - Rational Numbers

Chapter 2 - Linear Equations in One Variable

Chapter 4 - Practical Geometry

Chapter 5 - Data Handling

Chapter 6 - Squares and Square Roots

Chapter 7 - Cubes and Cube Roots

Chapter 8 - Comparing Quantities

Chapter 9 - Algebraic Expressions and Identities

Chapter 10 - Visualising Solid Shapes

Chapter 11 - Mensuration

Chapter 12 - Exponents and Powers

Chapter 13 - Direct and Inverse Proportions

Chapter 14 - Factorisation

Chapter 15 - Introduction to Graphs

Chapter 16 - Playing with Numbers

We Cover all the Given Exercises of Chapter 3 Understanding Quadrilaterals:-

Benefits of ncert solutions for class 8 maths chapter 3 understanding quadrilaterals.

Our subject specialists worked hard to make the solutions to NCERT Answers for Class 8 Mathematics Chapter 3 Understanding Quadrilaterals easier to comprehend for students. We have answered all of the questions from the chapter in the NCERT textbook. Students will be able to recognise the problems and solve them correctly in the test if they refer to these solutions.

Quick Revision 

Quadrilaterals are majorly of 6 types - Squares, Rectangles, Parallelograms, Trapeziums, Rhombuses, and Kites. It is important that students learn the formulas of area and perimeter for these quadrilaterals. It is also imperative that they revise the same so that they can use these to solve sums from this chapter quickly and efficiently.

List of Formulas

There are two major kinds of formulas related to quadrilaterals - Area and Perimeter. The following tables depict the formulas related to the areas and perimeters of different kinds of quadrilaterals.

Area of Quadrilaterals

Perimeter of quadrilaterals.

Perimeter of any quadrilateral is equal to the sum of all its sides, that is, AB + BC + CD + AD.

In conclusion, NCERT Solutions for Class 8 Maths Chapter 3 - Understanding Quadrilaterals provide a comprehensive and detailed understanding of the properties and characteristics of various types of quadrilaterals. By studying this chapter and using the NCERT solutions, students can enhance their knowledge of quadrilaterals and develop their problem-solving abilities.

The chapter begins by introducing the concept of a quadrilateral and its different types, such as parallelograms, rectangles, squares, rhombuses, and trapeziums. Each type is explained in terms of its defining properties, including sides, angles, diagonals, and symmetry.

FAQs on NCERT Solutions for Class 8 Maths Chapter 3 - Understanding Quadrilaterals

1. What is the Area of a Field in the Shape of a Rectangle with Dimensions of 20 Meters and 40 Meters?

We know that the field is rectangular. Hence, we can apply the area of a rectangle to find the field area.

Length of the field = 40 Metre

Width of the field = 20 Metre

Area of the rectangular field = Length × Width = 40 × 20 = 800 Sq. Meters.

We know if the length of the rectangle is L and breadth is B then,

Area of a rectangle = Length × Breadth or L × B

Perimeter = 2 × (L + B)

So, the properties and formulas of quadrilaterals that are used in this question:

Area of the Rectangle = Length × Width

So, we used only a specific property to find the answer.

2. Find the Rest of the Angles of a Parallelogram if one Angle is 80°?

For a parallelogram ABCD, as we know the properties:

The summation of any two adjacent angles = 180 degrees.

So, the angles opposite to the provided 80° angle will likewise be 80°.

Like we know, know that the Sum of angles of any quadrilateral = 360°.

So, if ∠A = ∠C = 80° then,

Sum of ∠A, ∠B, ∠C, ∠D = 360°

Also, ∠B = ∠D

Sum of 80°, ∠B, 80°, ∠D = 360°

Or, ∠B +∠ D = 200°

Hence, ∠B = ∠D = 100°

Now, we found all the angles of the quadrilateral, which are:

3. Why are the NCERT Solutions for Class 8 Maths Chapter 3 important?

The questions included in NCERT Solutions for Chapter 3 of Class 8 Maths are important not only for the exams but also for the overall understanding of quadrilaterals. These questions have been answered by expert teachers in the subject as per the NCERT (CBSE) guidelines. As the students answer the exercises, they will grasp the topic more comfortably and in a better manner.

4. What are the main topics covered in NCERT Solutions for Class 8 Maths Chapter 3?

All the topics of the syllabus of Class 8 Maths Chapter 3 have been dealt with in detail in the NCERT Solutions by Vedantu. The chapter is Understanding Quadrilaterals and has four exercises. All the important topics in Quadrilaterals have also been carefully covered. Students can also refer to the important questions section to get a good idea about the kind of questions usually asked in the exam.

5. Do I need to practice all the questions provided in the NCERT Solutions Class 8 Maths “Understanding Quadrilaterals”?

It helps to solve as many questions as possible because Mathematics is all about practice. If you solve all the practice questions and exercises given in NCERT Solutions for Class 8 Maths, you will be able to score very well in your exams comfortably. This will also help you understand the concepts clearly and allow you to apply them logically in the questions.

6. What are the most important concepts that I need to remember in Class 8 Maths Chapter 3?

For Class 8 Maths Chapter 3, you must remember the definition, characteristics and properties of all the quadrilaterals prescribed in the syllabus, namely, parallelogram, rhombus, rectangle, square, kite, and trapezium. Also know the properties of their angles and diagonals. Regular practise will help students learn the chapter easily.

7. Is Class 8 Maths Chapter 3 Easy?

Class 8 chapter 3 of Maths is a really interesting but critical topic. It's important not only for the Class 8 exams but also for understanding future concepts in higher classes. So, to stay focused and get a good grip of all concepts, it is advisable to download the NCERT Solutions for Class 8 Maths from the Vedantu website or from the Vedantu app at free of cost. This will help the students to clear out any doubts and allow them to excel in the exams. 

NCERT Solutions for Class 8 Maths

Ncert solutions for class 8.

Modal title

Your test/worksheet, discuss/report a question, quick summary of problem/doubt, detailed comments/doubts about this question, share a question, assignment remarks, remarks/comments, give accolades, release score.

• Understanding Quadrilaterals

NCERT curriculum (for CBSE/ICSE) Class 8 - Understanding Quadrilaterals

Unlimited worksheets.

Every time you click the New Worksheet button, you will get a brand new printable PDF worksheet on Understanding Quadrilaterals . You can choose to include answers and step-by-step solutions.

Unlimited Online Practice

Unlimited adaptive online practice on Understanding Quadrilaterals . Practice that feels like play! Get shields, trophies, certificates and scores. Master Understanding Quadrilaterals as you play.

Unlimited Online Tests

Take unlimited online tests on Understanding Quadrilaterals . Get instant scores and step-by-step solutions on submission. Make sure you always get your answers right in Understanding Quadrilaterals .

Create customized worksheets and tests to suit your needs.

Contents: Understanding Quadrilaterals

Questions related to Quadrilaterals and Polygons

Smaller topics in Understanding Quadrilaterals

Edugain login, welcome to edugain personalized math learning system., login using.

Forgot Password?

Register using

• Select your grade Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 11 Grade 12

Select your country

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Unit 3: Understanding quadrilaterals

• Polygons as special curves (Opens a modal)
• Open and closed curves Get 3 of 4 questions to level up!
• Polygon types Get 3 of 4 questions to level up!

Angle sum property

• Sum of interior angles of a polygon (Opens a modal)
• Sum of the exterior angles of a polygon (Opens a modal)
• Angles of a polygon Get 3 of 4 questions to level up!
• Interior and exterior angles of a polygon Get 3 of 4 questions to level up!

Kinds of quadrilaterals

• Intro to quadrilateral (Opens a modal)
• Quadrilateral types (Opens a modal)
• Kites as a geometric shape (Opens a modal)
• Analyze quadrilaterals Get 3 of 4 questions to level up!
• Quadrilateral types Get 3 of 4 questions to level up!

Properties of a parallelogram

• Proof: Opposite sides of a parallelogram (Opens a modal)
• Proof: Opposite angles of a parallelogram (Opens a modal)
• Proof: Diagonals of a parallelogram (Opens a modal)
• Side and angle properties of a parallelogram (level 1) Get 3 of 4 questions to level up!
• Side and angle properties of a parallelogram (level 2) Get 3 of 4 questions to level up!
• Diagonal properties of parallelogram Get 3 of 4 questions to level up!

Some special parallelograms

• Proof: Rhombus diagonals are perpendicular bisectors (Opens a modal)
• Rhombus diagonals (Opens a modal)

• CBSE Notes For Class 8
• CBSE Notes Class 8 Maths
• Chapter 3: Understanding Quadrilaterals

Understanding Quadrilaterals Class 8 Notes- Chapter 3

Cbse class 8 maths chapter 3 understanding quadrilaterals notes:- download pdf here.

To access the complete solutions for class 8 Maths chapter 3 understanding quadrilaterals, click on the below link.

• NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals . 

Introduction to Class 8 Understanding Quadrilaterals

In class 8, the chapter “Understanding Quadrilaterals”, will discuss the fundamental concepts related to quadrilaterals, different types of quadrilaterals and their properties, different types of curves, polygons and some of the theorems related to quadrilaterals such as angle sum property of quadrilaterals, and so on, with complete explanation.

What are Quadrilaterals?

Quadrilaterals are one type of polygon which has four sides and four vertices and four angles along with 2 diagonals. There are various types of quadrilaterals.

For more information on Quadrilaterals, watch the below video.

To know more about Quadrilaterals, visit here .

Types of Quadrilaterals

The classification of quadrilaterals are dependent on the nature of sides or angles of a quadrilateral and they are as follows:

• Parallelogram

The figure given below represents the properties of different quadrilaterals.

For more information on Types of Quadrilaterals, watch the below video.

Revisiting Geometry

As we know, Geometry is one of the branches of Mathematics, that deals with the study of different types of shapes, their properties, and how to construct lines, angles and different polygons. Geometry is broadly classified into plane geometry(two-dimensional) and solid geometry (three-dimensional geometry).

For more information on Geometry, watch the below video.

Introduction to Curves

A curve is a geometrical figure obtained when a number of points are joined without lifting the pencil from the paper and without retracing any portion. It is basically a line which need not be straight .

The various types of curves are:

• Open curve: An open curve is a curve in which there is no path from any of its point to the same point .
• Closed curve: A closed curve is a curve that forms a path from any of its point to the same point .

A curve can be :

• A closed curve:

•  An open curve:

• Simple open and closed curves:

  To know more about Curve, visit here .

A simple closed curve made up of only line segments is called a polygon . Various examples of polygons are Squares, Rectangles, Pentagons etc. Note: The sides of a polygon do not cross each other.

Classification of Polygons on the Basis of Number of Sides / Vertices

Polygons are classified according to the number of sides they have. The following lists the different types of polygons based on the number of sides they have:

• When there are three sides, it is  triangle
• When there are four sides, it is  quadrilateral
• When there are fives sides, it is  pentagon
• When there are six sides, it is  hexagon
• When there are seven sides, it is  heptagon
• When there are  eight sides, it is octagon
• When there are nine sides, it is  nonagon
• When there are ten sides, it is  decagon

For more information on Polygons, watch the below video.

To know more about Polygons and their Different Types, visit here .

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

Polygons on the Basis of Shape

Polygons can be classified as concave or convex based on their shape.

• A concave polygon is a polygon in which at least one of its interior angles is greater than 90 ∘ . Polygons that are concave have at least some portions of their diagonals in their exterior .
• A convex polygon is a polygon with all its interior angle less than 180 ∘ . Polygons that are convex have no portions of their diagonals in their exterior .

To know more about convex and concave polygons, click on the below links:

• Convex Polygon
• Concave Polygon

Polygons on the Basis of Regularity

Polygons can also be classified as regular polygons and irregular polygons  on the basis of regularity.

• When a polygon is both equilateral and equiangular it is called as a regular polygon. In a regular polygon, all the sides and all the angles are equal. Example: Square
• A polygon which is not regular i.e. it is not equilateral and equiangular, is an irregular polygon. Example: Rectangle

To know more about regular and irregular polygons, click here .

Angle Sum Property of a Polygon

According to the angle sum property of a polygon, the sum of all the interior angles of a polygon is equal to ( n − 2 ) × 180 ∘ , where n  is the number of sides of the polygon.

As we can see for the above quadrilateral, if we join one of the diagonals of the quadrilateral, we get two triangles. The sum of all the interior angles of the two triangles is equal to the sum of all the interior angles of the quadrilateral, which is equal to 360 ∘ = ( 4 − 2 ) × 180 ∘ . So, if there is a polygon which has n  sides , we can make ( n – 2) non-overlapping triangles which will perfectly cover that polygon.

The sum of the interior angles of the polygon will be equal to the sum of the interior angles of the triangles = ( n − 2 ) × 180 ∘

To know more about the Angle Sum Property of a Triangle, watch the below video

To know more about the sum of angles in a polygon, click here .

Sum of Measures of Exterior Angles of a Polygon

The sum of the measures of the external angles of any polygon is 360 ∘ .

Properties of Parallelograms

The following are the important properties of parallelogram:

• The opposite sides of a parallelogram are equal and congruent.
• Diagonals of a parallelogram bisect each other.
• The diagonals of parallelogram bisect each other and produce two congruent triangles
• The opposite angles of a parallelogram are congruent.

To learn more about the properties of parallelograms, click here .

For more information on Properties of Parallelogram, watch the below video.

Elements of a Parallelogram

• There are four sides and four angles in a parallelogram.
• The opposite sides and opposite angles of a parallelogram are equal .
• In the parallelogram ABCD, the sides ¯ ¯¯¯¯¯¯ ¯ A B and ¯ ¯¯¯¯¯¯¯ ¯ C D are opposite sides and the sides  ¯ ¯¯¯¯¯¯ ¯ A B and  ¯ ¯¯¯¯¯¯ ¯ B C are adjacent sides .
• Similarly, ∠ A B C and ∠ A D C are opposite angles and   ∠ A B C and ∠ B C D are adjacent angles .

Angles of a Parallelogram

The opposite angles of a parallelogram are equal . In the parallelogram ABCD, ∠ A B C = ∠ A D C and ∠ D A B = ∠ B C D .

The  adjacent angles in a parallelogram are supplementary . ∴ In the parallelogram ABCD, ∠ A B C + ∠ B C D = ∠ A D C + ∠ D A B = 180 ∘

For example, 

In the given parallelogram (RING), ∠R = 70°. Now, we have to find the remaining angles.

As we know, the opposite angles of a parallelogram are equal, we can write:

 ∠R = ∠N = 70°.

And we know, the adjacent angles of a parallelogram are supplementary, we get

 ∠R + ∠I = 180°

Hence, ∠I = 180° – 70° = 110°

Therefore, ∠I = ∠G = 110° [Since ∠I and ∠G are opposite angles]

Hence the angles of a parallelogram are ∠R = ∠N = 70° and ∠I = ∠G = 110°.

Diagonals of a Parallelogram

The diagonals of a parallelogram bisect each other at the point of intersection. In the parallelogram ABCD given below, OA = OC and OB = OD.

Consider an example, if OE = 4cm and HL is five more than PE, find the measure of OH.

Given that, OE = 4 cm and hence, OP = 4cm [Since OE = OP]

Hence PE =OE + OP = 4cm + 4cm = 8 cm

Also given that, HL is 5 more than PE, 

Hence, HL = 5 + 8 = 13 cm.

Therefore, OH = HL/2 = 13/2 = 6.5 cm

Therefore, the measurement of OH is 6.5 cm

Properties of Special Parallelograms

A rectangle is a parallelogram with equal angles and each angle is equal to 90 ∘ . Properties:

• Opposite sides of a rectangle are parallel and  equal .
• The length of diagonals of a rectangle is equal .
• All the interior angles of a rectangle are equal to 90 ∘ .
• The diagonals of a rectangle bisect each other at the point of intersection.

To know more about rectangles, click here .

For More Information On Rectangle, Watch The Below Video.

A square is a rectangle with equal sides . All the properties of a rectangle are also true for a square. In a square the diagonals:

• bisect one another
• are of equal length
• are perpendicular to one another

To learn more about squares, click here .

Rhombus is one of the special cases of parallelogram. In Rhombus, all the sides are equal and the opposite sides are also equal.

To learn more about rhombus, click here .

Frequently Asked Questions on CBSE Class 8 Maths Notes Chapter Understanding Quadrilaterals

What is a curve.

A curve refers to a line that is not straight. In other words, it may be any line that is bent to some extent.

What is a convex polygon?

Convex polygon is a polygon each of whose angles is less than a straight angle.

What are the properties of a Parallelogram?

1. Opposite sides are congruent 2. Opposite angels are congruent 3. Consecutive angles are supplementary. 4. Daigonals of a parallelogram bisect

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

• Understanding Quadrilaterals

NCERT curriculum (for CBSE/ICSE) Class 8 - Understanding Quadrilaterals

Unlimited worksheets.

Every time you click the New Worksheet button, you will get a brand new printable PDF worksheet on Understanding Quadrilaterals . You can choose to include answers and step-by-step solutions.

Unlimited Online Practice

Unlimited adaptive online practice on Understanding Quadrilaterals . Practice that feels like play! Get shields, trophies, certificates and scores. Master Understanding Quadrilaterals as you play.

Unlimited Online Tests

Take unlimited online tests on Understanding Quadrilaterals . Get instant scores and step-by-step solutions on submission. Make sure you always get your answers right in Understanding Quadrilaterals .

Contents: Understanding Quadrilaterals

Understanding Quadrilaterals - Questions related to Quadrilaterals and Polygons

AssignmentsBag.com

Assignments For Class 8 Mathematics Understanding Quadrilaterals

Assignments for Class 8 Mathematics Understanding Quadrilaterals have been developed for Standard 8 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 8 Mathematics Understanding Quadrilaterals from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 8 Mathematics Understanding Quadrilaterals. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Understanding Quadrilaterals book and get good marks in class 8 exams.

Assignments for Class 8 Mathematics Understanding Quadrilaterals as per CBSE NCERT pattern

All students studying in Grade 8 Mathematics Understanding Quadrilaterals should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics Understanding Quadrilaterals exam for standard 8. We have made sure that all topics given in your textbook for Mathematics Understanding Quadrilaterals which is suggested in Class 8 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

Some advantages of Free Assignments for Class 8 Mathematics Understanding Quadrilaterals

• Solving Assignments for Mathematics Understanding Quadrilaterals Class 8 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
• By solving one assignments given in your class by Mathematics Understanding Quadrilaterals teacher for class 8 will help you to keep in touch with the topic thus reducing dependence on last minute studies
• You will be able to understand the type of questions which are expected in your Mathematics Understanding Quadrilaterals class test
• You will be able to revise all topics given in the ebook for Class 8 Mathematics Understanding Quadrilaterals as all questions have been provided in the question banks
• NCERT Class 8 Mathematics Understanding Quadrilaterals Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 8 Mathematics Understanding Quadrilaterals teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 8 Mathematics Understanding Quadrilaterals Assignments PDF.

Free PDF download of Understanding Quadrilaterals Class 8 Worksheets with answers pdf created by master educators from the latest syllabus of CBSE Boards. By practicing these Understanding Quadrilaterals Class 8 Worksheet Pdf will help you to score more marks in your CBSE Board Examinations. We also give free NCERT Solutions and other study materials for students to make their preparation better.

Students who are searching for better solutions can download the Understanding Quadrilaterals Class 8 Worksheets with answers pdf to assist you with revising the whole syllabus and score higher marks in your exam.

This Understanding Quadrilaterals Class 8 Worksheets with answers pdf shows up with an answer key with step-by-step answers for students to comprehend the problem at each level and ​not retain it.

You can download free assignments for class 8 Mathematics Understanding Quadrilaterals from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 8 Mathematics Understanding Quadrilaterals from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 8, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

You can easily get question banks, topic wise notes and questions and other useful study material from https://www.assignmentsbag.com without any charge

Yes all test papers for Mathematics Understanding Quadrilaterals Class 8 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

https://www.assignmentsbag.com is the best portal to download all assignments for all classes without any charges.

Related Posts

Assignments For Class 3 Moral Science

Assignments For Class 3

Assignments For Class 10 Japanese

• Andhra Pradesh
• Chhattisgarh
• West Bengal
• Madhya Pradesh
• Maharashtra
• Jammu & Kashmir
• NCERT Books 2022-23
• NCERT Solutions
• NCERT Notes
• NCERT Exemplar Books
• NCERT Exemplar Solution
• States UT Book
• School Kits & Lab Manual
• NCERT Books 2021-22
• NCERT Books 2020-21
• NCERT Book 2019-2020
• NCERT Book 2015-2016
• RD Sharma Solution
• TS Grewal Solution
• TR Jain Solution
• Selina Solution
• Frank Solution
• ML Aggarwal Solution
• Lakhmir Singh and Manjit Kaur Solution
• I.E.Irodov solutions
• ICSE - Goyal Brothers Park
• ICSE - Dorothy M. Noronhe
• Sandeep Garg Textbook Solution
• Micheal Vaz Solution
• S.S. Krotov Solution
• Evergreen Science
• KC Sinha Solution
• ICSE - ISC Jayanti Sengupta, Oxford
• ICSE Focus on History
• ICSE GeoGraphy Voyage
• ICSE Hindi Solution
• ICSE Treasure Trove Solution
• Thomas & Finney Solution
• SL Loney Solution
• SB Mathur Solution
• P Bahadur Solution
• Narendra Awasthi Solution
• MS Chauhan Solution
• LA Sena Solution
• Integral Calculus Amit Agarwal Solution
• IA Maron Solution
• Hall & Knight Solution
• Errorless Solution
• Pradeep's KL Gogia Solution
• OP Tandon Solutions
• Sample Papers
• Previous Year Question Paper
• Value Based Questions
• CBSE Syllabus
• CBSE MCQs PDF
• Assertion & Reason
• New Revision Notes
• Revision Notes
• HOTS Question
• Marks Wise Question
• Toppers Answer Sheets
• Exam Paper Aalysis
• Concept Map
• CBSE Text Book
• Additional Practice Questions
• Vocational Book
• CBSE - Concept
• KVS NCERT CBSE Worksheets
• Formula Class Wise
• Formula Chapter Wise
• JEE Crash Course
• JEE Previous Year Paper
• Important Info
• JEE Mock Test
• JEE Sample Papers
• SRM-JEEE Mock Test
• VITEEE Mock Test
• BITSAT Mock Test
• Manipal Engineering Mock Test
• AP EAMCET Previous Year Paper
• COMEDK Previous Year Paper
• GUJCET Previous Year Paper
• KCET Previous Year Paper
• KEAM Previous Year Paper
• Manipal Previous Year Paper
• MHT CET Previous Year Paper
• WBJEE Previous Year Paper
• AMU Previous Year Paper
• TS EAMCET Previous Year Paper
• SRM-JEEE Previous Year Paper
• VITEEE Previous Year Paper
• BITSAT Previous Year Paper
• UPSEE Previous Year Paper
• CGPET Previous Year Paper
• CUSAT Previous Year Paper
• AEEE Previous Year Paper
• Crash Course
• Previous Year Paper
• NCERT Based Short Notes
• NCERT Based Tests
• NEET Sample Paper
• Previous Year Papers
• Quantitative Aptitude
• Numerical Aptitude Data Interpretation
• General Knowledge
• Mathematics
• Agriculture
• Accountancy
• Business Studies
• Political science
• Enviromental Studies
• Mass Media Communication
• Teaching Aptitude
• NAVODAYA VIDYALAYA
• SAINIK SCHOOL (AISSEE)
• Mechanical Engineering
• Electrical Engineering
• Electronics & Communication Engineering
• Civil Engineering
• Computer Science Engineering
• CBSE Board News
• Scholarship Olympiad
• School Admissions
• Entrance Exams
• All Board Updates
• Miscellaneous
• State Wise Books
• Engineering Exam

Understanding Quadrilaterals Assignment 9 Worksheet Class 8 PDF with Answers

These Understanding Quadrilaterals Assignment 9 worksheet PDF can be helpful for both teachers and students. Teachers can track their student’s performance in the chapter Understanding Quadrilaterals Assignment 9. Students can easily identify their strong points and weak points by solving questions from the worksheet. Accordingly, students can work on both weak points and strong points. 

All students studying in CBSE class 8th, need to practise a lot of questions for the chapter Understanding Quadrilaterals Assignment 9. Students can easily practise questions from the Understanding Quadrilaterals Assignment 9 problems worksheet PDF. By practising a lot of questions, students can improve their confidence level. With the help of confidence level, students can easily cover all the concepts included in the chapter Understanding Quadrilaterals Assignment 9. 

Understanding Quadrilaterals Assignment 9 Worksheets with Solutions

Solutions is the written reply for all questions included in the worksheet. With the help of Understanding Quadrilaterals Assignment 9 worksheets with solutions, students can solve all doubts regarding questions. Students can have deep learning in the chapter Understanding Quadrilaterals Assignment 9 by solving all their doubts. By solving doubts, students can also score well in the chapter Understanding Quadrilaterals Assignment 9. 

Understanding Quadrilaterals Assignment 9 Worksheet PDF

Worksheet is a sheet which includes many questions to solve for class 8th students. The Understanding Quadrilaterals Assignment 9 worksheet PDF provides an opportunity for students to enhance their learning skills. Through these skills, students can easily score well in the chapter Understanding Quadrilaterals Assignment 9. Students can solve the portable document format (PDF) of the worksheet from their own comfort zone. 

How to Download the Understanding Quadrilaterals Assignment 9 Worksheet PDF? 

To solve questions from the Understanding Quadrilaterals Assignment 9 worksheet PDF, students can easily go through the given steps. Those steps are- 

• Open Selfstudys website.

• Bring the arrow towards CBSE which can be seen in the navigation bar. 

• Drop down menu will appear, select KVS NCERT CBSE Worksheet. 

• A new page will appear, select class 8th from the given list of classes. 
• Select Mathematics from the given list of subjects. Now click the chapter’s name that is Understanding Quadrilaterals Assignment 9. 

Features of the Understanding Quadrilaterals Assignment 9 Worksheet PDF

Before starting to solve questions from the Understanding Quadrilaterals Assignment 9 problems worksheet PDF, students need to know everything about the worksheet. Those features are- 

• Variety of questions are included:  The Understanding Quadrilaterals Assignment 9 Maths Worksheet for Class 8 includes varieties of questions. Those varieties of questions are- one mark questions, two mark questions, three mark questions, etc. 
• Solutions are provided:  Doubts regarding each question can be easily solved through the solutions given. Through solving questions, a student's comprehensive skill can be increased. 
• All concepts are covered:  By solving questions from the Understanding Quadrilaterals Assignment 9 problems worksheet, students can easily cover all the concepts included in the chapter.  
• Created by Expert:  These worksheets are personally created by the subject experts. These Understanding Quadrilaterals Assignment 9 worksheet pdf are created with proper research. 
• Provides plenty of questions:  The Understanding Quadrilaterals Assignment 9 worksheet provides plenty of questions to practise. Through good practice, students can get engaged in the learning process. 

Benefits of the Understanding Quadrilaterals Assignment 9 Worksheet PDF

With the help of Understanding Quadrilaterals Assignment 9 problems worksheet PDF, students can easily track their performance. This is the most crucial benefit, other than this there are more benefits. Those benefits are- 

• Builds a strong foundation:  Regular solving questions from the worksheet can help students to build a strong foundation. Through the strong foundation, students can score well in the chapter Understanding Quadrilaterals Assignment 9. 
• Improves speed and accuracy:  While solving questions from the chapter Understanding Quadrilaterals Assignment 9, students need to maintain the speed and accuracy. Speed and accuracy can be easily maintained and improved by solving questions from the Understanding Quadrilaterals Assignment 9 worksheet PDF. 
• Acts as a guide:  Understanding Quadrilaterals Assignment 9 worksheets with solutions acts as guide for both the teachers and students. Through the worksheet, teachers can guide their students according to the answers given by them. Students can also analyse themselves with the help of answers and can improve accordingly. 
• Enhances the learning process:  Regular solving of questions from the worksheet can help students enhance their learning process. According to the learning skills, students can easily understand all topics and concepts included in the chapter Understanding Quadrilaterals Assignment 9.  
• Improvisation of grades:  Regular solving of questions from the worksheet can help students to improve their marks and grades. With the help of good marks and good grades, students can select their desired field further. 

Tips to Score Good Marks in Understanding Quadrilaterals Assignment 9 Worksheet

Students are requested to follow some tips to score good marks in the Understanding Quadrilaterals Assignment 9 worksheet. Those tips are-

• Complete all the concepts:  First and the most crucial step is to understand all the concepts included in the chapter Understanding Quadrilaterals Assignment 9.  
• Practise questions:  Next step is to practise questions from the Understanding Quadrilaterals Assignment 9 problems worksheet. Through this students can identify all types of questions: easy, moderate, difficult, etc.  
• Note down the mistakes:  After practising questions, students need to note down the wrong sums that have been done earlier. 
• Rectify the mistakes:  After noting down the mistakes, students need to rectify all the mistakes made. 
• Maintain a positive attitude:  Students are requested to maintain a positive attitude while solving worksheets. By maintaining a positive attitude, students can improve speed and accuracy while solving the worksheets. 
• Remain focused:  Students need to remain focused while solving questions from the Understanding Quadrilaterals Assignment 9 problems worksheet pdf. As it helps students to solve the questions as fast as possible. 

When should a student start solving the Understanding Quadrilaterals Assignment 9 Worksheet PDF?

Students studying in class 8 should start solving worksheets after covering each and every concept included in the chapter. Regular solving questions from the Understanding Quadrilaterals Assignment 9 worksheet PDF, can help students to have a better understanding of the chapter. Better understanding of the chapter Understanding Quadrilaterals Assignment 9 can help students to score well in the class 8th board exam. 

Regular solving questions from the Understanding Quadrilaterals Assignment 9 Worksheet PDF can help students to build a strong foundation for the chapter Understanding Quadrilaterals Assignment 9. Strong foundation of the chapter Understanding Quadrilaterals Assignment 9 can help students to understand further chapters. 

• NCERT Solutions for Class 12 Maths
• NCERT Solutions for Class 10 Maths
• CBSE Syllabus 2023-24
• Social Media Channels
• Login Customize Your Notification Preferences

One Last Step...

• Second click on the toggle icon

Provide prime members with unlimited access to all study materials in PDF format.

Allow prime members to attempt MCQ tests multiple times to enhance their learning and understanding.

Provide prime users with access to exclusive PDF study materials that are not available to regular users.