NCERT Solutions for Class 8 Maths Chapter 3: Understanding Quadrilaterals - Exercise 3.4

Exercise 3.4

Refer to pages 22-24 for exercise 3.4 in the PDF

1. State whether True or False.

(a) All rectangles are squares.

Ans: This statement is false.

Because all squares are rectangles but all rectangles are not square.

As in square, all sides are equal.

But in rectangles opposite sides are equal.

(b) All rhombuses are parallelograms.

Ans: This statement is true.

Because opposite sides are equal and opposite sides are parallel in a rhombus.

(c) All squares are rhombuses and also rectangles.

Ans: This statement is true.

Because in rhombuses opposite sides are equal and parallel, so as in square.

In a rectangle opposite sides are equal and parallel, so as in square.

(d) All squares are not parallelograms.

Ans: This statement is false.

All squares are parallelograms.

Because in a square all sides are equal and opposite sides are parallel.

(e) All kites are rhombuses.

Ans: This statement is false.

Because in kites opposite sides are not equal. The Diagonal top of the kite is not equal.

(f) All rhombuses are kites.

Ans:This statement is true.

As rhombuses also have two consecutive sides they are equal as in kite.

(g) All parallelograms are trapeziums.

Ans: This statement is true.

Because all parallelograms have pairs of parallel sides.

(h) All squares are trapeziums.

Ans: This statement is true.

Because all squares have a pair of parallel sides.

2. Identify all the quadrilaterals that have

(a) four sides of equal length

Ans: Square and rhombuses are the quadrilaterals which have all four sides of equal length.

(b) four right angles

Ans: Square and rectangle are the quadrilaterals which have all four angles.

3. Explain how a square is.

(i) a quadrilateral

Ans: A square is quadrilateral because it has four sides.

(ii) a parallelogram

Ans: A square is parallelogram because it’s opposite sides are of equal length and parallel. And opposite angles of the square are also equal.

(iii) a rhombus

Ans: A square rhombus is a square because the square has all sides of equal length.

(iv) a rectangle

Ans: A square is a rectangle because opposite sides are of equal length and all angles are right angles.

4. Name the quadrilaterals whose diagonals.

(i) bisect each other

Ans: Square, rectangle, rhombus and parallelogram are the quadrilaterals in which diagonals bisect each other.

(ii) are perpendicular bisectors of each other

Ans: Square and rhombus are the quadrilaterals in which diagonals are perpendicular bisectors of each other.

(iii) are equal

Ans: Rectangle, square and parallelogram are the quadrilaterals in which diagonals are equal.

5. Explain why a rectangle is a convex quadrilateral.

Ans: Rectangle is a convex quadrilateral because both diagonals of the rectangle are lying inside of the rectangle.

6. ABC is a right-angled 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).

Ans:

(Image Will Be Updated Soon)

Given :\[ABC\] is a right angle triangle in which \[\angle B\] is right angle and \[O\] is a mid-point of \[AC\] .

Construction : Draw line \[AD{\text{ and }}DC\]such that \[AD\parallel BC\]and \[AB\parallel DC\] .

And, \[AB = DC,{\text{ }}AD = BC\]

(Image Will Be Updated Soon)

As, opposite sides are of equal length, opposite sides are parallel and also all interior angles are measure of \[90^\circ \].

Therefore, \[ABCD\] is a rectangle.

So, in a rectangle, diagonals of equal length bisect each other.

Therefore,

\[AO = OC = BO = OD\]

Hence, \[O\] is equidistant from \[A,B{\text{ and }}C\].

Class 8 Maths Chapter 3 Exercise 3.4 – In a Nutshell

‘Quadrilaterals’ is a crucial chapter for students as it deals with various shapes and sizes of things that we use in our daily life. Mostly those go unnoticed; however, gaining knowledge about some specific mathematical shapes is a bonus. It will help you ace your exam as well as create an impact on your regular life as well.  

Also, taking note of your daily life will further simplify the learning procedure. On the other hand, you can also refer to our NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4 for an extensive explanation of the chapter. Our solutions are composed of elabo0rate descriptions starting from the fundamentals of every Mathematical shape included in this chapter.

Comprehensive learning of the same will help you in gaining an insight into the terminologies used while answering the questions. Here, you will also learn about the basics of every shape, other than quadrilaterals. They are:

• Circles

• Triangles

• Cone

• Rhombus

• Kite 

Having clarity of the fundamental differences between these figures is essential beforehand, as it will help in building a strong foundation for the subject on all. However, you can always have a look at our Class 8 Maths Exercise 3.4 study materials offered by Vedantu. 

They are not only standard notes, but also available online for your ready reference whenever you require. You may even cross-check your solutions with the solutions provided in the study materials of NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4. From our notes, you can learn the below mentioned:

• Develop an in-depth understanding of a topic.

• Get shortcut tricks for solving numerical.

• Avail tabular form of essential data for faster memorisation.

• Obtain valid reasoning behind every subjective explanation.

• Minimise potential errors.

Hence, our solutions can help you in building an overall grip on the chapter, which will, in turn, help you in improving your scores as well. Nevertheless, below here is an overview of all exercises covered in this chapter, with a particular focus on Class 8 Maths Solution Exercise 3.4.

NCERT Class 8 Maths Exercise 3.4 - Question 1

You are given eight statements here, and you have to decide if they are true or not. All the given statements are facts based on various quadrilaterals. Hence, students should have the facts cleared in their mind to determine whether the given statements are correct.

To gain appropriate clarity, you can take a look at our NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4, where you will find detailed explanations for each of the mathematical shapes that come under quadrilaterals –

• Rectangles

• Squares

• Rhombus

• Parallelogram

• Kite

• Trapezium 

Also, a proper comparison is necessary between each of these shapes, so that you can differentiate them based on their properties. In our NCERT Solution Class 8 Maths Chapter 3 Exercise 3.4, you will find shortcut techniques to memorise the facts quickly and correctly. 

Also, we have provided valid reasons behind the truthfulness/falseness of a statement. Consequently, you can answer the questions as well, without making any mistakes. It will also boost your scores in exams too.

Class 8 Maths Chapter 3 Exercise 3.4 - Question 2

The second question is interesting as it acts like a riddle. There are two clues given, and you are asked to identify the quadrilateral it refers to. To decipher the information behind each clue, you need to be thorough with the properties of various shapes in quadrilaterals. 

To de-clutter the data and approach the question in the right path, you can have a look at our NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4 for a quick revision before your actual exam. We have explained each clue and the approach you should take to reach the end of the question and arrive at a correct solution. 

Also, our solutions are so crafted, as to help you in dealing with every twisted question that might be asked in the actual exam. This NCERT Solution for Class 8 Maths Exercise 3.4 will help you in being prepared for any tricky question as well as in handling them appropriately.

Class 8 Maths Chapter 3 Exercise 3.4 - Question 3

Question 3 is entirely based on the properties of a square. You have to show how a square can be all the following mathematical shapes –

• A quadrilateral

• A parallelogram

• A rhombus

• A rectangle

The main objective is here to prove that a square is similar to these shapes in some of the other aspects. Therefore, students should have prior understanding of all these shapes too along with square to be able to draw a suitable comparison.

For an in-depth analysis, go through our NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4, which has listed all the relevant properties of these shapes separately and also in a tabular form to draw a comparison. 

The tabular form will help you in memorising the properties. Hence, drawing out the relevant information based on similarities between different shapes also becomes easier. Also, you will not have to worry about committing any errors.

NCERT Class 8 Maths Exercise 3.4 - Question 4

In question 4, you have to name the quadrilaterals based on the three clues given. Each clue corresponds to a particular quadrilateral. More importantly, the clues are based on a specific property of that shape – it’s diagonal.

The three different cases given are when the diagonals are –

• Equal

• Bisect each other

• Perpendicularly bisect each other

While answering these, you can find two new terms as bisector and perpendicular bisector. Students should know the primary difference between these two and that they are not the same. Our NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4 will assist you in developing these concepts.

Also, they should know what does that figure is called wherein; they cut each other or are equal. All these properties are extensively explained in our Maths NCERT Solutions Class 8 Chapter 3 Exercise 3.4 with appropriate diagrams to facilitate a better understanding of the same.

Class 8 Maths Exercise 3.4 - Question 5

This question goes a little deeper into the concept of a quadrilateral as you are introduced to two new types – convex and concave. Students have to develop an overall idea of this concept, starting from the grassroots. 

Herein, you are asked to explain why a rectangle is called a convex quadrilateral. To cite a valid reason to this, you should have prior understanding of both the terms as well as how it can be accorded to a specific quadrilateral, as presented in our NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4. 

Our tutors recommend that you can follow the following steps for a natural outcome:

• Assess the properties of a regular quadrilateral.

• List the properties of the specific shape which is to be compared.

• Tally them both and find the junction point (common).

You can also consider our study materials for Class 8 Maths Solution Exercise 3.4 to gain knowledge about the same comprehensively.

Class 8 Maths Chapter 3 Exercise 3.4 - Question 6

It is the last question in this exercise, and here you are provided with a figure of a triangle, which is projected with dotted lines to form a quadrilateral. As a result, the figure contains two diagonals now with a mid-point, and you are asked to reason why are the lines joining the vertices are equidistant from the centre.

From our NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4, you can know how these types of questions can be answered most readily. There, you will get a detailed solution to this question is a step by step method.

The criteria are mentioned one after another, along with valid reasons for each so that you can understand them well. As a result, you will be prepared to tackle any tricky question if the situation arises.

Class 8 Maths Chapter 3 Exercise 3.4 – Other Exercises

We provide solutions to other exercises included in this chapter. Here is a brief overview of the same.

• Exercise 3.1: In this exercise, you have to solve seven questions wherein you will learn about:

1. Various types of curves and polygon shapes like hexagons.

2. Parallel lines and lines cutting them at different points.

3. Angles formed on parallel lines.

4. Relation between the angles.

5. Concept of a trapezium.

• Exercise 3.2: Six questions are asked in this exercise, based on concepts of angles and degrees. You have to find the missing values (degrees) of a polygon. Essential parts of this exercise that are explained in our NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4 are as follows:

1. Exterior and interior angles.

2. Sum of all angles of a polygon.

3. Types of regular polygons.

4. Minimum and maximum possible interior and exterior angle of a specific polygon.

5. Measurement of angles in various types of triangles. 

• Exercise 3.3: It has twelve questions to be answered and based on a variety of concepts triangles and quadrilaterals. You can refer to our Ex 3.4 Class 8 NCERT Solutions for a clear understanding of the following:

1. Identifying triangles out of a quadrilateral.

2. Determining angles of a parallelogram.

3. Properties of a parallelogram based on its sides and angles.

4. Supplementary and complementary angles.

5. Comparison of rectangle and parallelogram. 

All these three exercises are based on inter-linked concepts; for instance, properties related to angles, sides and diagonals of specific quadrilaterals. You might also be asked to prove certain theorems and/or statements in specific questions as well. Only proper clarity on these topics will help you in answering these questions quickly.

We have provided NCERT Solution of Maths Class 8 Chapter 3 Exercise 3.4with valid reasons alongside. Also, alternate methods are given along, so as to allow you to choose the one which you are comfortable with. These study notes of NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.4 are not only equipped to help you understand, but also build a strong foundation of Maths.

So, you can completely do away with any doubt while studying before the exam, just by referring to these notes by Vedantu for a more fundamental understanding. As they are available online, you can download them for free and after that, access them anytime.

All these features of our study material fulfil our aim of providing a superior learning experience to students. Above all, a regular practice of such questions will help you in acing the exam with higher grades.

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