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Case Study Questions for Class 8 Maths Chapter 3 Understanding Quadrilaterals
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Here we are providing Case Study questions for Class 8 Maths Chapter 3 Understanding Quadrilaterals.
Maths Class 8 Chapter 3  Understanding Quadrilaterals. 

CBSE Class 8  
Class 8 Maths Chapter 3  
Case Study Questions  
Yes, answers provided  
Provided in the end 
Case Study Questions
Related posts, learning outcomes.
 Convex and Concave Polygons.
 Regular and Irregular Polygons.
 Sum of Measures of the Exterior Angles of a Polygon.
 Kinds of QuadrilateralTrapezium; Kite; Parallelogram.
 Some Special ParallelogramsRhombus; Rectangle; Square.
Important Keywords
 Convex Polygon: Polygons that have any line segment joining any two different points in the interior and have no portions of their diagonals in their exteriors are called convex polygons.
 Concave Polygon: Polygons that have one diagonal outside it are called concave polygons.
 Regular Polygon: A polygon whose all sides, all angles are equal that is which is both equiangular and equilateral are called regular polygon. Example: Square; Equilateral triangle
 Irregular Polygon: Polygon whose all sides are not equal are called Irregular polygon. Example: Rectangle.
Fundamental Facts
 Convex Polygon has each angle either acute or obtuse.
 Concave Polygon has one angle as reflex angle.
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 Understanding Quadrilaterals Class 8 Case Study Questions Maths Chapter 3
Last Updated on April 30, 2024 by XAM CONTENT
Hello students, we are providing case study questions for class 8 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 8 maths. In this article, you will find case study questions for CBSE Class 8 Maths Chapter 3 Understanding Quadrilaterals. It is a part of Case Study Questions for CBSE Class 8 Maths Series.
Understanding Quadrilaterals  
Case Study Questions  
Competency Based Questions  
CBSE  
8  
Maths  
Class 8 Studying Students  
Yes  
Mentioned  
Table of Contents
Case Study Questions on Understanding Quadrilaterals
There is a trapezium MNOP, angle bisector of ∠M and ∠N meet at point W, and angle bisector of ∠O and ∠P meet at point X on side MN of trapezium MNOP.
By using the figure give the answers to following questions:
Q. 1. What is the value of a? (a) 80° (b) 60° (c) 90° (d) 70°
Ans. Option (b) is correct. Explanation: In Triangle XPO, ∠XPO = 50° (XP is angle bisector of ∠X) ∠XOP = 70° (XO is angle bisector of ∠XPO) ∠XOP + ∠XPO + a = 180° 70° + 50° + a = 180° a = 180°– 120° a = 60°
Q. 2. What is the value of d? (a) 70° (b) 60° (c) 80° (d) 90°
Ans. Option (d) is correct. Explanation: ∠O + ∠N = 180° (sum of adjacent angles of trapezium is 180°)
Q. 3. What is the value of c? (a) 90° (b) 70° (c) 50° (d) 80°
Ans. Option (a) is correct. Explanation: ∠P + ∠M = 180° (sum of adjacent angles of trapezium is 180°)
Q. 4. What type of triangle is POX?
Ans. In triangle POX, All angles are less than 90°, therefore it is an acute angle triangle.
Q. 5. What is the value of b?
Ans. In quadrilateral XYWZ, a + b + y +z = 360° c = y = 90° (vertically opposite angles are equal) d = z = 90° (vertically opposite angles are equal) 60° + b + 90°+ 90° = 360° b = 120°
Linear Equations in One Variable Class 8 Case Study Questions Maths Chapter 2
Rational numbers class 8 case study questions maths chapter 1, topics from which case study questions may be asked.
 Convex and Concave Polygons.
 Regular and Irregular Polygons.
 Sum of Measures of the Exterior Angles of a Polygon.
 Kinds of QuadrilateralTrapezium; Kite; Parallelogram.
 Some Special ParallelogramsRhombus; Rectangle; Square.
Frequently Asked Questions (FAQs) on Understanding Quadrilaterals Case Study
Q1: why understanding quadrilaterals are important.
A1: Understanding quadrilaterals is crucial for building a strong foundation in geometry, enabling realworld applications in design and construction. It enhances problemsolving skills, fosters critical thinking, and prepares students for advanced mathematical concepts and career opportunities.
Q2: What is a quadrilateral?
A2: A quadrilateral is a polygon with four sides and four angles.
Q3: What are the different types of quadrilaterals?
A3: There are various types of quadrilaterals, including squares, rectangles, parallelograms, rhombuses, trapeziums, and kites.
Q4: How do you classify quadrilaterals based on their properties?
A4: Quadrilaterals can be classified based on their properties such as sides, angles, and diagonals. For example: (1) Parallelograms have opposite sides that are equal and parallel. (2) Rhombuses have all four sides equal in length. (3) Rectangles have all angles equal to 90 degrees.
Q5: What is the sum of angles in a quadrilateral?
A5: The sum of angles in any quadrilateral is always 360 degrees.
Q6: Can a quadrilateral have equal sides and angles but still not be a square?
A6: Yes, a rhombus can have all sides equal and opposite angles equal, but its angles need not be right angles, unlike in a square.
Q7: How do you prove that a quadrilateral is a parallelogram?
A7: A quadrilateral can be proved as a parallelogram if its opposite sides are equal and parallel, or if its opposite angles are equal.
Q8: What is the difference between a square and a rhombus?
A8: A square is a type of rhombus with all four sides equal and all angles equal to 90 degrees. However, a rhombus may have all sides equal but not necessarily all angles equal to 90 degrees.
Q9: What do you mean by convex polygon?
A9: Polygons that have any line segment joining any two different points in the interior and have no portions of their diagonals in their exteriors are called convex polygons.
Q10: What do you mean by concave polygon?
A10: Polygons that have one diagonal outside it are called concave polygons.
Q11: What do you mean by regular polygon?
A11: A polygon whose all sides, all angles are equal that is which is both equiangular and equilateral are called regular polygon. Example: Square; Equilateral triangle
Q12: What do you mean by irregular polygon?
A12: Polygon whose all sides are not equal are called Irregular polygon. Example: Rectangle.
Q13: Are there any online resources or tools available for practicing understanding quadrilaterals case study questions?
A13: We provide case study questions for CBSE Class 8 Maths on our website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.
Q14: What are the important points to note for CBSE Class 8 Maths Understanding Quadrilaterals?
A14: Here are some important points to observe/note (i) Every parallelogram is a trapezium, but every trapezium is not a parallelogram. (ii) Every rectangle, rhombus and square are parallelograms, but every parallelogram is not a rectangle or a rhombus or a square. (iii) Every square is a rectangle, but every rectangle is not a square. (iv) Every square is a rhombus, but every rhombus is not a square
Related Posts
NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals
NCERT solutions for class 8 maths chapter 3 understanding quadrilaterals define a polygon as a simple closed curve that is made up of straight lines. Thus, a quadrilateral can be defined as a polygon that has four sides, four angles, and four vertices. This chapter starts by introducing children to some very important concepts that they need to learn before moving on to studying quadrilaterals . These topics include the classification of polygons on the basis of sides, examining diagonals , concave, convex, regular, and irregular polygons as well as the angle sum property. The scope of NCERT solutions class 8 maths chapter 3 is very vast as there are several properties and types of quadrilaterals available. However, the explanation given in these solutions helps to simplify the learning process ensuring that students can build a strong geometrical foundation.
Class 8 maths NCERT solutions chapter 3 elaborates on special quadrilaterals such as squares , rectangles , parallelograms , kites , and rhombuses . They show kids how to solve problems based on these figures and intelligently utilize the associated properties to remove the complexities from such questions. In the NCERT solutions Chapter 3 Understanding Quadrilaterals we will take an indepth look at the basic elements and theories of these foursided polygons and also you can find some of these in the exercises given below.
 NCERT Solutions Class 8 Maths Chapter 3 Ex 3.1
 NCERT Solutions Class 8 Maths Chapter 3 Ex 3.2
 NCERT Solutions Class 8 Maths Chapter 3 Ex 3.3
 NCERT Solutions Class 8 Maths Chapter 3 Ex 3.4
NCERT Solutions for Class 8 Maths Chapter 3 PDF
Using the NCERT solutions class 8 maths children can solidify several concepts of quadrilaterals. They understand the conditions under which a special quadrilateral such as a parallelogram becomes a square, how to find the measure of an interior or exterior angle , and so on. The links to all these brief and precise solutions are given below and kids can use them to improve their mathematical acumen.
☛ Download Class 8 Maths NCERT Solutions Chapter 3 Understanding Quadrilaterals
NCERT Class 8 Maths Chapter 3 Download PDF
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals
Quadrilaterals form a vital shape contributing to geometrical studies. Thus, children need to develop a robust conceptual foundation as they will require it in higher classes for solving more complicated problems and constructing this figure. They can do this by revising the solutions given above regularly. The following sections deal with an exercisewise detailed analysis of NCERT Solutions Class 8 Maths Chapter 3 understanding quadrilaterals.
 Class 8 Maths Chapter 3 Ex 3.1  7 Questions
 Class 8 Maths Chapter 3 Ex 3.2  6 Questions
 Class 8 Maths Chapter 3 Ex 3.3  12 Questions
 Class 8 Maths Chapter 3 Ex 3.4  6 Questions
☛ Download Class 8 Maths Chapter 3 NCERT Book
Topics Covered: Identifying the polygon, finding the measure of angles, and verifying the exterior angles of a polygon are topics under class 8 maths NCERT solutions chapter 3. Apart from this, there are many sections dealing with the various elements of trapeziums , parallelograms, rectangles, squares, etc.
Total Questions: There are a total of 31 fantastic sums in Class 8 maths chapter 3 Understanding Quadrilaterals. 7 are simple theorybased problems, 16 are inbetween and 8 are higherorder thinking sums.
List of Formulas in NCERT Solutions Class 8 Maths Chapter 3
The questions in the NCERT solutions class 8 maths chapter 3 are not only based on some formulas but also see the use of various vital properties. The sum of interior and exterior angles , along with theorems give the keys to attempting these sums. The angle sum property states that the sum of all the interior angles of a polygon is a multiple of the number of triangles that make up that polygon. Such pointers covered in NCERT solutions for class 8 maths chapter 3 make up the crux of this lesson and are given below.
 Angle Sum Property of a Quadrilateral: a + b + c + d = 360°. (a, b, c, d are the interior angles).
 The opposite sides and opposite angles of a parallelogram are equal in length.
 The adjacent angles in a parallelogram are supplementary.
 The diagonals of a parallelogram bisect each other.
 The diagonals of a rhombus are perpendicular bisectors of one another.
Important Questions for Class 8 Maths NCERT Solutions Chapter 3
CBSE Important Questions for Class 8 Maths Chapter 3 Exercise 3.1 

CBSE Important Questions for Class 8 Maths Chapter 3 Exercise 3.2 

CBSE Important Questions for Class 8 Maths Chapter 3 Exercise 3.3 

CBSE Important Questions for Class 8 Maths Chapter 3 Exercise 3.4 

NCERT Solutions for Class 8 Maths Video Chapter 3
NCERT Class 8 Maths Videos for Chapter 3  

Video Solutions for Class 8 Maths Exercise 3.1  
Video Solutions for Class 8 Maths Exercise 3.2  
Video Solutions for Class 8 Maths Exercise 3.3  
Video Solutions for Class 8 Maths Exercise 3.4  
FAQs on NCERT Solutions Class 8 Maths Chapter 3
Do i need to practice all questions provided in ncert solutions class 8 maths understanding quadrilaterals.
All the sums in the NCERT Solutions Class 8 Maths Understanding Quadrilaterals cover different subtopics of the lesson. These sums also pave a foundation for the geometrical topics in grades that are to follow. Thus, it is crucial for kids to practice all questions so as to get a clear idea of all the components in a quadrilateral.
What are the Important Topics Covered in Class 8 Maths NCERT Solutions Chapter 3?
Each exercise is based on a different topic such as angles of a polygon, rhombus, square, and rectangles; thus, each section that falls under the NCERT Solutions Class 8 Maths Chapter 3 must be given equal importance. Kids need to strategize their studies to focus more on learning properties and then applying them to questions.
How Many Questions are there in NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals?
There are a total of 31 questions in the NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals that are distributed among 4 exercises. There are different types of questions such as true and false sums, identifying the type of shape based on certain properties, and finding the measure of a particular angle using formulas.
What are the Important Formulas in Class 8 Maths NCERT Solutions Chapter 3?
Formulas such as the angle sum property of a quadrilateral, exterior angle property of a polygon, and other associated theories form the foundation of the NCERT Solutions Class 8 Maths Chapter 3. Students must spend a good amount of time practicing questions so as to get a good understanding of their application.
How CBSE Students can utilize NCERT Solutions Class 8 Maths Chapter 3 effectively?
To effectively utilize NCERT Solutions Class 8 Maths Chapter 3 it is advised that students go through the theory and solved examples associated with each exercise. They should then try to attempt the problem on their own. Finally, to get the best out of these solutions kids should crosscheck their answers and go through the steps so that they can organize their answers in a wellstructured manner.
Why Should I Practice NCERT Solutions Class 8 Maths Understanding Quadrilaterals Chapter 3?
The only way to ensure that a student has perfected his knowledge of a chapter is by practicing the questions periodically. The NCERT Solutions Class 8 Maths Understanding Quadrilaterals Chapter 3 has been given by experts with certain tips included to simplify the problems. By regular revision, kids will be confident with the topic and can get an amazing score in their examination.
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NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals
 NCERT Solutions
 Chapter 3 Understanding Quadrilaterals
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals  FREE PDF Download
The NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals covers all the chapter's questions (All Exercises). These NCERT Solutions for Class 8 Maths have been carefully compiled and created in accordance with the most recent CBSE Syllabus 202425 updates. Students can use these NCERT Solutions for Class 8 to reinforce their foundations. Subject experts at Vedantu have created the continuity and differentiability class 8 NCERT solutions to ensure they match the current curriculum and help students while solving or practising problems.
Glance of NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals  Vedantu
In this article, we will learn about different quadrilaterals like squares, rectangles, parallelograms, rhombuses, and trapeziums, along with their properties.
This chapter dives into the world of quadrilaterals, which are foursided closed figures.
This chapter explains effective methods to solve problems concerning quadrilaterals.
Each type of quadrilateral is discussed in terms of its defining properties including side lengths, angle measurements, diagonals, and symmetry.
The chapter also highlights special properties of certain quadrilaterals, like the properties of diagonals in rectangles and squares, and the diagonals of rhombuses.
This article contains chapter notes, formulas, exercise links, and important questions for chapter 3  Understanding Quadrilaterals.
There are four exercises (26 fully solved questions) in Class 8th Maths Chapter 3 Understanding Quadrilaterals.
Access Exercise Wise NCERT Solutions for Chapter 3 Maths Class 8
Current Syllabus Exercises of Class 8 Maths Chapter 3 




Exercises Under NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals
Exercise 3.1 introduces polygons, covering their basic definition and classification based on the number of sides, such as triangles, quadrilaterals, pentagons, etc. It also distinguishes between convex and concave polygons, helping students understand the differences between these types of polygons.
Exercise 3.2 delves into the properties of quadrilaterals, exploring various types like trapeziums, kites, and parallelograms. This exercise helps students learn to identify different quadrilaterals and understand their specific properties.
Exercise 3.3 examines the properties of parallelograms, such as opposite sides being equal and parallel, opposite angles being equal, and diagonals bisecting each other. It includes problems for identifying parallelograms based on these properties and proving certain properties using theorems.
Exercise 3.4 looks at special parallelograms like rhombuses, rectangles, and squares. It highlights their unique properties, such as all sides being equal in a rhombus and all angles being 90 degrees in a rectangle. This exercise helps students understand and differentiate between these specific types of parallelograms.
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
Area of a Square  Side x Side 
Area of a Rectangle  Length x Width 
Area of a Parallelogram  Base x Height 
Area of a Rhombus  1/2 x 1st Diagonal x 2nd Diagonal 
Area of a Kite  1/2 x 1st Diagonal x 2nd Diagonal 
Perimeter of Quadrilaterals
Perimeter of any quadrilateral is equal to the sum of all its sides, that is, AB + BC + CD + AD.
Name of the Quadrilateral  Perimeter 
Perimeter of a Square  4 x Side 
Perimeter of a Rectangle  2 (Length + Breadth) 
Perimeter of a Parallelogram  2 (Base + Side) 
Perimeter of a Rhombus  4 x Side 
Perimeter of a Kite  2 (a + b), where a and b are the adjacent pairs 
Access NCERT Solutions for Class 8 Maths 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. What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides (ii) 4 sides (iii) 6 sides
Solution: A regular polygon is a flat shape with all sides of equal length and all interior 5angles equal in measure. In simpler terms, all the sides are the same size and all the corners look the same.
Here are the names of regular polygons based on the number of sides:
(i) 3 sides  Equilateral Triangle (all three angles are also 60 degrees each)
(ii) 4 sides  Square
(iii) 6 sides  Hexagon
Exercise3.2
1. Find ${\text{x}}$in the following figures.
We need to find the value of ${\text{x}}{\text{.}}$
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.
Exercise 3.4
1. State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.
Every square is indeed a type of rectangle, not every rectangle can be called a square.
It's correct to say that all squares can be classified as parallelograms due to their shared characteristic of having opposite sides that are parallel and opposite angles that are equal.
Because, a kite shape is that its adjacent sides are not necessarily equal in length, unlike those of a square.
2. Identify all the quadrilaterals that have.
(a) four sides of equal length
(b) four right angles
(a) Rhombus and square have all four sides of equal length.
(b) Square and rectangles have four right angles.
3. Explain how a square is
(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle
(i) Square is a quadrilateral because it has four sides.
(ii) A square is a parallelogram because its opposite sides are parallel and opposite angles are equal.
(iii) Square is a rhombus because all four sides are of equal length and diagonals bisect at right angles.
(iv)Square is a rectangle because each interior angle, of the square, is 90°
4. Name the quadrilaterals whose diagonals.
(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal
(i) Parallelogram, Rhombus, Square and Rectangle
(ii) Rhombus and Square
(iii)Rectangle and Square
5. Explain why a rectangle is a convex quadrilateral.
A rectangle is a convex quadrilateral because both of its diagonals lie inside the rectangle.
6. ABC is a rightangled triangle and O is the midpoint of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).
AD and DC are drawn so that AD  BC and AB  DC
AD = BC and AB = DC
ABCD is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of 90°.
In a rectangle, diagonals are of equal length and also bisect each other.
Hence, AO = OC = BO = OD
Thus, O is equidistant from A, B and C.
Overview of Deleted Syllabus for CBSE Class 8 Maths Understanding Quadrilaterals
Chapter  Dropped Topics 
Understanding Quadrilaterals  3.1 Introduction 
3.2 Polygons  
3.2.1 Classification of polygons  
3.2.2 Diagonals  
3.2.5 Angle sum property. 
Class 8 Maths Chapter 3: Exercises Breakdown
Exercise  Number of Questions 
Exercise 3.1  2 Questions & Solutions (1 Long Answer, 1 Short Answer) 
Exercise 3.2  6 Questions & Solutions (6 Short Answers) 
Exercise 3.3  12 Questions & Solutions (6 Long Answers, 6 Short Answers) 
Exercise 3.4  6 Questions & Solutions (1 Long Answer, 5 Short Answers) 
In conclusion, NCERT Solutions for Class 8 Maths Chapter 3  Understanding Quadrilaterals provides 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 problemsolving abilities. The chapter starts by introducing quadrilaterals and their diverse types, including parallelograms, rectangles, squares, rhombuses, and trapeziums. It goes on to explain each type, detailing their characteristic properties like side lengths, angles, diagonals, and symmetry. Students that practice these kinds of questions will gain confidence and perform well on tests.
Other Study Material for CBSE Class 8 Maths Chapter 3
S.No.  Important links for Class 8 Maths Chapter 3 Understanding Quadrilaterals 
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ChapterSpecific NCERT Solutions for Class 8 Maths
Given below are the chapterwise NCERT Solutions for Class 8 Maths . Go through these chapterwise solutions to be thoroughly familiar with the concepts.
S.No.  NCERT Solutions Class 8 ChapterWise Maths PDF 
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3 

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FAQs on NCERT Solutions 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:
Opposite angles are equal.
Opposite sides are equal and parallel.
Diagonals bisect each other.
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.
8. In Maths Class 8 Chapter 3, how are quadrilaterals used in everyday life?
Quadrilaterals are everywhere! Here are some examples:
Shapes in your house: Doors, windows, tabletops, picture frames, book covers, even slices of bread are quadrilaterals (mostly rectangles).
Construction and design: Architects use rectangles and squares for walls, floors, and windows. Roads and bridges often involve trapezoids and other quadrilaterals for support.
Everyday objects: Stop signs, traffic signals, and many sports fields (like baseball diamonds) are quadrilaterals.
9. How many quadrilaterals are there in Class 8 Chapter 3 Maths?
There are many types of quadrilaterals mentioned in Class 8 Understanding Quadrilaterals, but some of the most common include:
Rectangle (all four angles are 90 degrees, opposite sides are equal and parallel)
Square (a special rectangle with all sides equal)
Parallelogram (opposite sides are parallel)
Rhombus (all four sides are equal)
Trapezoid (one pair of parallel sides)
10. What are real examples of quadrilaterals in Class 8 Chapter 3 Maths?
Some real examples of quadrilaterals are:
Rectangle: Doorway, window pane, sheet of paper, tabletop, chocolate bar, playing card (most common)
Square: Dice, coaster, napkin, wall tiles (when all sides are equal)
Parallelogram: Textbook cover, kite (when opposite sides are parallel), solar panel
Rhombus: Traffic warning sign (diamond shape with all sides equal)
Trapezoid: Slice of pizza, roof truss (one pair of parallel sides)
Irregular Quadrilateral: Flag (many flags like the US flag are not perfectly symmetrical quadrilaterals)
11. How do you identify a quadrilateral in Maths Class 8 Chapter 3?
A quadrilateral has the following properties:
Four straight sides
Four angles (interior angles add up to 360 degrees)
Four vertices (corners where two sides meet)
NCERT Solutions for Class 8 Maths
Ncert solutions for class 8.
NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12
Understanding Quadrilaterals Class 8 Extra Questions Maths Chapter 3
July 7, 2019 by Sastry CBSE
Extra Questions for Class 8 Maths Chapter 3 Understanding Quadrilaterals
Understanding Quadrilaterals Class 8 Extra Questions Very Short Answer Type
Question 4. The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of each angle. Solution: Sum of all interior angles of a quadrilateral = 360° Let the angles of the quadrilateral be 2x°, 3x°, 5x° and 8x°. 2x + 3x + 5x + 8x = 360° ⇒ 18x = 360° ⇒ x = 20° Hence the angles are 2 × 20 = 40°, 3 × 20 = 60°, 5 × 20 = 100° and 8 × 20 = 160°.
Understanding Quadrilaterals Class 8 Extra Questions Short Answer Type
Question 15. Write true and false against each of the given statements. (a) Diagonals of a rhombus are equal. (b) Diagonals of rectangles are equal. (c) Kite is a parallelogram. (d) Sum of the interior angles of a triangle is 180°. (e) A trapezium is a parallelogram. (f) Sum of all the exterior angles of a polygon is 360°. (g) Diagonals of a rectangle are perpendicular to each other. (h) Triangle is possible with angles 60°, 80° and 100°. (i) In a parallelogram, the opposite sides are equal. Solution: (a) False (b) True (c) False (d) True (e) False (f) True (g) False (h) False (i) True
Understanding Quadrilaterals Class 8 Extra Questions Higher Order Thinking Skills (HOTS)
Extra Questions for Class 8 Maths
Ncert solutions for class 8 maths, free resources.
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Chapter 3 Class 8 Understanding Quadrilaterals
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Get NCERT Solutions of Chapter 3 Class 8 Understanding Quadrilaterals free at teachoo. Answers to all exercise questions and examples have been solved, with concepts of the chapter explained.
In this chapter, we will learn
 What are curves , open curves, closed curves, simple curves
 What are polygons , Different Types of Polygons
 Diagonal of a Polygon
 Convex and Concave Polygons
 Regular and Irregular Polygons
 Angle Sum Property of Polygons
 Sum of Exterior Angles of a Polygon
 Exterior Angles of a Regular Polygon
 What is a Quadrilateral
 Parallelogram
 Parallelogram propertie s  Opposite Angles are equal, Opposite sides are equal, Adjacent Angles are supplementary, Diagonals Bisect Each other
 Rhombus, Rectangle, Square are all parallelograms with additional properties
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Unit 6: Quadrilateral : Constructions and Types
Kinds of quadrilaterals.
 Intro to quadrilaterals (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)
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. To score good marks in Class 8 Mathematics examination, it is advised to solve questions provided at the end of each chapter in the NCERT book.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals are prepared based on Class 8 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration. Further, all the CBSE Class 8 Solutions Maths Chapter 3 are in accordance with the latest CBSE guidelines and marking schemes.
Class 8 Maths Chapter 3 Exercise 3.1 Solutions
Class 8 Maths Chapter 3 Exercise 3.2 Solutions
Class 8 Maths Chapter 3 Exercise 3.3 Solutions
Class 8 Maths Chapter 3 Exercise 3.4 Solutions
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NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals
Ncert solutions for class 8 maths chapter 3 understanding quadrilaterals pdf download.
Study Materials for Class 8 Maths Chapter 3 Understanding Quadrilaterals 

 Exercise 3.1 Chapter 3 Class 8 Maths NCERT Solutions
 Exercise 3.2 Chapter 3 Class 8 Maths NCERT Solutions
 Exercise 3.3 Chapter 3 Class 8 Maths NCERT Solutions
 Exercise 3.4 Chapter 3 Class 8 Maths NCERT Solutions
NCERT Solutions for Class 8 Maths Chapters:
How many exercises in Chapter 3 Understanding Quadrilaterals
What is equilateral triangle, in a quadrilateral abcd, the angles a, b, c and d are in the ratio 1 : 2 : 3 : 4. find the measure of each angle of the quadrilateral., the interior angle of a regular is 108°. find the number of sides of the polygon., contact form.
 CBSEUnderstanding Quadrilaterals
 Sample Questions
Understanding QuadrilateralsSample Questions
 STUDY MATERIAL FOR CBSE CLASS 8 MATH
 Chapter 1  Algebraic Expressions and Identities
 Chapter 2  Comparing Quantities
 Chapter 3  Cubes and Cube Roots
 Chapter 4  Data handling
 Chapter 5  Direct and Inverse Proportions
 Chapter 6  Exponents and Powers
 Chapter 7  Factorization
 Chapter 8  Introduction to Graphs
 Chapter 9  Mensuration
 Chapter 10  Playing with Numbers
 Chapter 11  Practical Geometry
 Chapter 12  Squares and Square Roots
 Chapter 13  Visualizing Solid Shapes
 Chapter 14  Linear Equations in One Variable
 Chapter 15  Rational Numbers
 Chapter 16  Understanding Quadrilaterals
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8th Class Mathematics Understanding Quadrilaterals Question Bank
Done understanding quadrilaterals total questions  44.
question_answer 1) ABCD is a quadrilateral. If AC and BD bisect each other, what is ABCD?
A) A square done clear
B) A parallelogram done clear
C) A rectangle done clear
D) All the above done clear
question_answer 2) ABCD is a parallelogram. The angle bisectors of \[\angle A\] and \[\angle D\] meet at O. What is the measure of \[\angle AOD\]?
A) \[{{45}^{o}}\] done clear
B) \[{{90}^{o}}\] done clear
C) \[{{75}^{o}}\] done clear
D) \[{{180}^{o}}\] done clear
question_answer 3) The diagonal of a rectangle is \[10\text{ }cm\] and its breadth is\[6\text{ }cm\]. What is its length?
A) \[6\text{ }cm\] done clear
B) \[5\,\,cm\] done clear
C) \[8\,\,cm\] done clear
D) \[4\,\,cm\] done clear
A) \[p+q+r+s=w+x+y+z\] done clear
B) \[p+q+r+s<w+x+y+z\] done clear
C) \[p+q+r+s>w+x+y+z\] done clear
D) Either (B) or (C) done clear
question_answer 5) What do you call a parallelogram which has equal diagonals?
A) A trapezium done clear
B) A rectangle done clear
C) A rhombus done clear
D) A kite done clear
question_answer 6) In a square ABCD, the diagonals bisect at O. What type of a triangle is AOB?
A) An equilateral triangle. done clear
B) An isosceles but not a right angled triangle. done clear
C) A right angled but not an isosceles triangle. done clear
D) An isosceles right angled triangle. done clear
question_answer 7) The perimeter of a parallelogram is\[180\text{ }cm\]. If one side exceeds the other by \[10\text{ }cm,\] what are the sides of the parallelogram?
A) \[40\text{ }cm,\text{ }50\text{ }cm~\] done clear
B) \[45\text{ }cm\] each done clear
C) \[50\text{ }cm\] each done clear
D) \[45\text{ }cm,\text{ }50\text{ }cm\] done clear
question_answer 8) In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. What type of a quadrilateral is ABCD?
D) A trapezium done clear
A) \[{{90}^{o}}\] done clear
B) \[{{60}^{o}}\] done clear
C) \[{{45}^{o}}\] done clear
D) \[{{135}^{o}}\] done clear
question_answer 10) In a parallelogram ABCD, if \[AB=2x+5,\]\[CD~=y+1,\] \[AD=y+5~\] and \[BC=3x4,\]what is the ratio of AB and BC?
A) \[71:21\] done clear
B) \[12:11\] done clear
C) \[31:35\] done clear
D) \[4:7\] done clear
question_answer 11) If ABCD is an isosceles trapezium, what is the measure of \[\angle C\]?
A) \[\angle B\] done clear
B) \[\angle A\] done clear
C) \[\angle D\] done clear
D) \[{{90}^{o}}\] done clear
question_answer 12) A diagonal of a rectangle is inclined to one side of the rectangle at \[{{25}^{o}}\]. What is the measure of the acute angle between the diagonals?
A) \[{{25}^{o}}\] done clear
B) \[{{40}^{o}}\] done clear
C) \[{{50}^{o}}\] done clear
D) \[{{55}^{o}}\] done clear
question_answer 13) If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio \[3:7:6:4,\]what is PQRS?
A) A rhombus done clear
B) A parallelogram done clear
C) A trapezium done clear
A) A square done clear
B) A trapezium done clear
C) An isosceles trapezium done clear
D) A rectangle done clear
question_answer 15) If two adjacent angles of a parallelogram are in the ratio \[3:2,\]what are their measures?
A) \[{{108}^{o}},{{72}^{o}}\] done clear
B) \[{{72}^{o}},{{36}^{o}}\] done clear
C) \[{{100}^{o}},{{80}^{o}}\] done clear
D) \[{{144}^{o}},{{36}^{o}}\] done clear
A) \[{{60}^{o}}\] done clear
B) \[{{70}^{o}}\] done clear
C) \[{{80}^{o}}\] done clear
D) \[{{85}^{o}}\] done clear
A) \[2\] done clear
B) \[3\] done clear
C) \[3\] done clear
D) \[2\] done clear
A) \[12,5,13\] done clear
B) \[5,12,13\] done clear
C) \[5,13,5\] done clear
D) \[12,13,5\] done clear
A) \[{{100}^{o}},\text{ }{{80}^{o}},\text{ }{{100}^{o}}\] done clear
B) \[{{100}^{o}},\text{ }{{100}^{o}},\text{ }{{80}^{ol}},\] done clear
C) \[{{80}^{o}},{{100}^{o}},{{100}^{o}}\] done clear
D) \[{{80}^{o}},{{80}^{o}},{{100}^{o}}\] done clear
A) \[{{36}^{o}}\] done clear
B) \[{{72}^{o}}\] done clear
C) \[{{108}^{o}}\] done clear
D) \[{{120}^{o}}\] done clear
A) \[{{210}^{o}}\] done clear
B) \[{{110}^{o}}\] done clear
C) \[{{540}^{o}}\] done clear
D) \[{{105}^{o}}\] done clear
question_answer 22) Each interior angle of a regular polygon is \[{{150}^{o}}\] How many sides has the polygon?
A) \[8\] done clear
B) \[12\] done clear
C) \[9\] done clear
D) \[10\] done clear
A) \[{{30}^{o}}\] done clear
B) \[{{40}^{o}}\] done clear
C) \[{{60}^{o}}\] done clear
D) \[{{50}^{o}}\] done clear
A) \[{{100}^{o}}\] done clear
C) \[{{130}^{o}}\] done clear
D) \[{{120}^{o}}\] done clear
question_answer 25) Each interior angle of a regular polygon is \[{{162}^{o}}\] How many sides has the polygon?
A) \[12\] done clear
B) \[20\] done clear
C) \[16\] done clear
question_answer 26) ABCD is a quadrilateral such that \[AB=BC,\] \[AD=\frac{1}{2}CD\] and \[AD=\frac{1}{4}AB\]. If \[BC=12\text{ }cm,\]what is the measure of AD?
A) \[6\,cm\] done clear
B) \[4\,cm\] done clear
C) \[12\,cm\] done clear
D) \[3\,cm\] done clear
A) \[4\] done clear
B) \[3\sqrt{3}\] done clear
C) \[3\] done clear
D) \[5\] done clear
question_answer 28) How many measurements are required to construct a quadrilateral?
A) \[5\] done clear
B) \[4\] done clear
D) \[2\] done clear
question_answer 29) How many unique measurements are needed to construct a parallelogram?
A) \[2\] done clear
B) \[3\] done clear
C) \[4\] done clear
D) \[1\] done clear
question_answer 30) What is the minimum number of dimensions needed to construct a rectangle?
A) \[1\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
question_answer 31) What is the minimum number of measurements needed to construct a square?
B) \[2\] done clear
D) \[4\] done clear
A) \[{{15}^{o}}\] done clear
B) \[{{30}^{o}}\] done clear
C) \[{{45}^{o}}\] done clear
D) \[{{60}^{o}}\] done clear
A) A trapezium done clear
B) A rhombus done clear
C) A rectangle done clear
A) \[{{200}^{o}}\] done clear
B) \[{{270}^{o}}\] done clear
C) \[{{360}^{o}}\] done clear
D) \[{{540}^{o}}\] done clear
question_answer 35) In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA and OC?
A) \[\frac{OB}{OD}\] done clear
B) \[\frac{BC}{CD}\] done clear
C) \[\frac{AD}{AB}\] done clear
D) \[\frac{AC}{BD}\] done clear
question_answer 36) In \[\Delta ABC,\] P and Q are the midpoints of AB and AC. If PQ is produced to R such that \[PQ=QR,\]what is PRCB?
A) A rectangle done clear
B) A square done clear
C) A rhombus done clear
D) A parallelogram done clear
question_answer 37) Three angles of a quadrilateral are equal and the measure of the fourth angle is \[{{120}^{o}}\]. Find the measure of each of these equal angles.
A) \[{{80}^{o}}\] done clear
B) \[{{120}^{o}}\] done clear
C) \[{{60}^{o}}\] done clear
D) \[{{140}^{o}}\] done clear
question_answer 38) A quadrilateral has three acute angles, each measuring \[{{75}^{o}}\] Find the measure of the fourth angle.
A) \[{{65}^{o}}\] done clear
B) \[{{135}^{o}}\] done clear
C) \[{{140}^{o}}\] done clear
D) \[{{225}^{o}}\] done clear
B) \[{{110}^{o}}\] done clear
C) \[{{120}^{o}}\] done clear
D) \[{{130}^{o}}\] done clear
A) \[{{45}^{o}}\] done clear
C) \[{{255}^{o}}\] done clear
D) \[{{225}^{o}}\] done clear
A) \[{{28}^{o}}\] done clear
B) \[{{33}^{o}}\] done clear
C) \[{{55}^{o}}\] done clear
D) \[{{37}^{o}}\] done clear
A) \[{{47}^{o}}\] done clear
B) \[{{24}^{o}}\] done clear
C) \[{{67}^{o}}\] done clear
D) \[{{58}^{o}}\] done clear
A) \[{{105}^{o}}\] done clear
B) \[{{95}^{o}}\] done clear
C) \[{{135}^{o}}\] done clear
A) \[{{85}^{o}}\] done clear
B) \[{{65}^{o}}\] done clear
C) \[{{50}^{o}}\] done clear
D) \[{{130}^{o}}\] done clear
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Class 9 Maths Case Study Questions of Chapter 8 Quadrilaterals PDF Download
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Class 9 Maths Case Study Questions Chapter 8 are very important to solve for your exam. Class 9 Maths Chapter 8 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case studybased questions for Class 9 Maths Chapter 8 Quadrilaterals
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These case study questions challenge students to apply their knowledge of quadrilaterals in practical scenarios, enhancing their problemsolving abilities. This article provides the Class 9 Maths Case Study Questions of Chapter 8: Quadrilaterals, enabling students to practice and excel in their examinations.
Quadrilaterals Case Study Questions With Answers
Here, we have provided casebased/passagebased questions for Class 9 Maths Chapter 8 Quadrilaterals
Case Study/PassageBased Questions
Case Study 1: Laveena’s class teacher gave students some colorful papers in the shape of quadrilaterals. She asked students to make a parallelogram from it using paper folding. Laveena made the following parallelogram.
How can a parallelogram be formed by using paper folding? (a) Joining the sides of a quadrilateral (b) Joining the midpoints of sides of a quadrilateral (c) Joining the various quadrilaterals (d) None of these
Answer: (b) Joining the midpoints of sides of quadrilateral
Which of the following is true? (a) PQ = BD (b) PQ = 1/2 BD (c) 3PQ = BD (d) PQ = 2BD
Answer: (b) PQ = 1/2 BD
Which of the following is correct combination? (a) 2RS = BD (b) RS = 1/3 BD (c) RS = BD (d) RS = 2BD
Answer: (a) 2RS = BD
Which of the following is correct? (a) SR = 2PQ (b) PQ = SR (c) SR = 3PQ (d) SR = 4PQ
Answer: (b) PQ = SR
Case Study/Passage Based Questions
Case Study 2: Anjali and Meena were trying to prove midpoint theorem. They draw a triangle ABC, where D and E are found to be the midpoints of AB and AC respectively. DE was joined and extended to F such that DE = EF and FC is also joined.
▲ADE and ▲CFE are congruent by which criterion? (a) SSS (b) SAS (c) RHS (d) ASA
Answer: (b) SAS
∠EFC is equal to which angle? (a) ∠DAE (b) ∠EDA (c) ∠AED (d) ∠DBC
Answer: (b)∠EDA
∠ECF is equal to which angle? (a) ∠EAD (b) ∠ADE (c) ∠AED (d) ∠B
Answer: (a) ∠EAD
CF is equal to (a) EC (b) BE (c) BC (d) AD
Answer: (d) AD
CF is parallel to (a) AE (b) CE (c) BD (d) AC
Answer: (c) BD
Case Study 3. A group of students is exploring different types of quadrilaterals. They encountered the following scenario:
Four friends, Aryan, Bhavana, Chetan, and Divya, participated in a geometry project. They constructed a figure with four sides and made the following observations:
 The opposite sides of the figure are parallel.
 The opposite angles of the figure are congruent.
 The figure has two pairs of congruent adjacent sides.
 The sum of the measures of the interior angles of the figure is 360 degrees.
Based on this information, the students were asked to analyze the properties of the quadrilateral they constructed. Let’s see if you can answer the questions correctly:
MCQ Questions:
Q1. The type of quadrilateral formed by their figure is: (a) Parallelogram (b) Rhombus (c) Rectangle (d) Square
Answer: (a) Parallelogram
Q2. The measure of each angle in the figure is: (a) 90 degrees (b) 120 degrees (c) 135 degrees (d) 180 degrees
Answer: (d) 180 degrees
Q3. The figure is an example of a quadrilateral that satisfies the: (a) Opposite sides are equal condition (b) Opposite angles are congruent condition (c) Diagonals bisect each other condition (d) None of the above
Answer: (b) Opposite angles are congruent condition
Q4. The sum of the measures of the exterior angles of the figure is: (a) 90 degrees (b) 180 degrees (c) 270 degrees (d) 360 degrees
Answer: (d) 360 degrees
Q5. The figure has rotational symmetry of: (a) Order 1 (b) Order 2 (c) Order 3 (d) Order 4
Answer: (a) Order 1
Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 8 Quadrilaterals with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Quadrilaterals Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate
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Understanding Quadrilaterals. Maths: CBSE Class 8: Chapter Covered: Class 8 Maths Chapter 3: Topics: Sum of the measures of exterior angles of a Polygon Kinds of Quadrilaterals: Type of Questions: Case Study Questions: Questions with Answers: Yes, answers provided: Important Keywords: Provided in the end
A4: Quadrilaterals can be classified based on their properties such as sides, angles, and diagonals. For example: (1) Parallelograms have opposite sides that are equal and parallel. (2) Rhombuses have all four sides equal in length. (3) Rectangles have all angles equal to 90 degrees.
Class 8 Maths Chapter 3  Understanding Quadrilaterals  Case Study QuestionIn this video, I have solved case study question of class 8 maths chapter 3 Under...
Class 8 Chapter 3 Important Questions. Questions and answers are given here based on important topics of class 8 Maths Chapter 3. Q.1: A quadrilateral has three acute angles, each measure 80°. What is the measure of the fourth angle?
Unit test. Level up on all the skills in this unit and collect up to 700 Mastery points! Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, worldclass education for anyone, anywhere.
CBSE Class 8 Maths Important Questions for Understanding Quadrilaterals  Free PDF Download. Important Questions for Class 8 Chapter 3  Understanding Quadrilaterals is based upon the basic concepts of Quadrilaterals and the questions given in the segment by Vedantu will help students prepare for final exams.
According to NCERT Solutions for Class 8 Maths Chapter 3, a quadrilateral is a plane figure that has four sides or edges and also has four corners or vertices. Quadrilaterals will typically be of standard shapes with four sides like rectangle, square, trapezoid, and kite or irregular and uncharacterized shapes. Q3.
There are a total of 31 questions in the NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals that are distributed among 4 exercises. There are different types of questions such as true and false sums, identifying the type of shape based on certain properties, and finding the measure of a particular angle using formulas.
The NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals covers all the chapter's questions (All Exercises). These NCERT Solutions for Class 8 Maths have been carefully compiled and created in accordance with the most recent CBSE Syllabus 202425 updates. Students can use these NCERT Solutions for Class 8 to reinforce their ...
Question 3. In the given figure, find x. Question 4. The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of each angle. Let the angles of the quadrilateral be 2x°, 3x°, 5x° and 8x°. and 8 × 20 = 160°. Question 5. Find the measure of an interior angle of a regular polygon of 9 sides.
Some special parallelograms. Proof: Rhombus diagonals are perpendicular bisectors. Rhombus diagonals. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, worldclass education for anyone, anywhere.
Understanding Quadrilaterals Case Study Questions for Grade 8 NCERT CBSE chapter 3.#UnderstandingQuadrilaterals#UnderstandingQuadrilateralsCaseStudyQuestions...
Updated for new NCERT Book. Get NCERT Solutions of Chapter 3 Class 8 Understanding Quadrilaterals free at teachoo. Answers to all exercise questions and examples have been solved, with concepts of the chapter explained. In this chapter, we will learn. To learn from the NCERT, click on an exercise or example link below to get started.
Class 8. 14 units · 61 skills. Unit 1. Rational and irrational numbers. Unit 2. Parallel lines and transversal. Unit 3. Indices and cube roots. Unit 4. Expansion formulae. ... Analyze quadrilaterals Get 3 of 4 questions to level up! Quadrilateral types Get 3 of 4 questions to level up! Properties of a parallelogram. Learn. Proof: Opposite ...
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. To score good marks in Class 8 Mathematics examination, it is advised to solve questions provided at the end of each chapter in the NCERT book.
The classification of quadrilaterals are dependent on the nature of sides or angles of a quadrilateral and they are as follows: Trapezium. Kite. Parallelogram. Square. Rectangle. Rhombus. The figure given below represents the properties of different quadrilaterals.
Easy way to solve Case study questions#casestudy #NCERTMath8 #DAV #davmath8 #mathtricks #dav #8math #math @minakshimathsclassesCase study based Questions r...
MCQs Questions for Class 8 Maths Chapter 3 Understanding Quadrilaterals. Page No: 41. Exercise 3.1. 1. Given here are some figures. Classify each of them on the basis of the following. (a) Simple curve (b) Simple closed curve (c) Polygon. (d) Convex polygon (e) Concave polygon. Answer.
Why? 3. The perimeter of a parallelogram is 150 cm. One of its side is greater than the other by 25 cm. Find length of all sides of the parallelogram. 4. Lengths of adjacent sides of a parallelogram is 3 cm and 4 cm. Find its perimeter. 5. In a parallelogram, the ratio of the adjacent sides is 4 : 5 and its perimeter is 72 cm then, find the ...
Free Question Bank for 8th Class Mathematics Understanding Quadrilaterals Understanding Quadrilaterals. Customer Care : 6267349244. Toggle navigation 0 . 0 . Railways; UPSC; CET ... Study Package. Question  Understanding Quadrilaterals. Buy Now. Contact
Here, we have provided casebased/passagebased questions for Class 9 Maths Chapter 8 Quadrilaterals. Case Study/PassageBased Questions. Case Study 1: Laveena's class teacher gave students some colorful papers in the shape of quadrilaterals. She asked students to make a parallelogram from it using paper folding.
Answer: A.135°. Explanation: The adjacent angles of a parallelogram sums up to 180°. 20. The kite has exactly two distinct consecutive pairs of sides of equal length. Answer: A. True. Explanation: A kite is a quadrilateral that has exactly two distinct consecutive pairs of sides of equal length. Class 8 Maths Chapter 3 Understanding ...
Install Now. Case study questions for class 8 topic surface area and volume and understanding quadrilaterals. Report. Posted by Ankita Sharma 2 years, 4 months ago. CBSE > Class 09 > Mathematics. 0 answers. ANSWER. Arrange √2, ³√4, ⁴√5 and ⁴√3 in ascending order. Report.