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NCERT Solutions Class 6 Maths Chapter 5 Understanding Elementary Shapes

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Last updated date: 14th Jul 2024
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NCERT Solutions Chapter 5 Understanding Elementary Shapes Maths Class 6 - FREE PDF Download

Class 6 Maths NCERT Solutions for Chapter 5 Understanding Elementary Shapes which explains the fundamental shapes encountered before, like lines, triangles, and squares. Students will learn not only how to identify them but also how to compare their sizes, classify them based on their properties, and explore their angles.

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Table of Content
1. NCERT Solutions Chapter 5 Understanding Elementary Shapes Maths Class 6 - FREE PDF Download
2. Glance on Maths Chapter 5 Class 6 - Understanding Elementary Shapes
3. Access Exercise-wise NCERT Solutions for Chapter 5 Maths Class 6
4. Exercises Under NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes
5. Access NCERT Solutions for Class 6 Maths Chapter 5 – Understanding Elementary Shapes
6. Overview of Deleted Syllabus for CBSE Class 6 Maths Understanding Elementary Shapes
7. Class 6 Maths Chapter 5: Exercises Breakdown
8. Other Study Material for CBSE Class 6 Maths Chapter 5
9. Chapter-Specific NCERT Solutions for Class 6 Maths
FAQs


Class 6 Maths Chapter 5 PDF with Solution lays the foundation for your understanding of geometry, an interesting branch of mathematics that deals with shapes, sizes, and spatial relationships. With the help of these NCERT solutions, You will master the concepts presented in a clear and step-by-step manner, making your journey into the world of shapes both enjoyable and enriching! Access the latest CBSE Class 6 Maths Syllabus here.


Glance on Maths Chapter 5 Class 6 - Understanding Elementary Shapes

  • NCERT Solution for Chapter 5 Understanding Elementary Shapes Class 6 PDF covers topics such as Lines and Segments, Angles, Triangles, Quadrilaterals, and Circles.

  • Understanding different types of lines and learning how to measure them accurately and  discover special angles like right angles, acute angles, and obtuse angles.

  • Explore different types of triangles based on their side lengths and angles.

  • Get to know four-sided shapes like squares, rectangles, parallelograms, and more. We will uncover their unique properties and learn to differentiate between them.

  • Get acquainted with the circle, a perfectly round shape with some special features.

  • This article contains chapter notes, important questions, exemplar solutions, exercises, and video links for Chapter 5 - Understanding Elementary Shapes, which you can download as PDFs.

  • There are eight exercises (43 fully solved questions) in class 6th maths chapter 6 Pair of Linear Equations in Two Variables.


Access Exercise-wise NCERT Solutions for Chapter 5 Maths Class 6

Exercises Under NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Exercise 5.1: Measuring Line Segments

This exercise focuses on measuring line segments accurately using a ruler. Students learn to measure different lengths and understand the importance of precision in geometry.


Exercises 5.2, 5.3, and 5.4: Types of Angles

Students explore angles, such as acute, obtuse, right, straight, reflex, and complete angles. They learn to identify and draw these angles using a protractor.


Exercise 5.5: Perpendicular Lines

This exercise focuses on identifying and drawing perpendicular lines. Students learn the concept of perpendicularity, how to use a set square to draw perpendicular lines, and the properties of perpendicular lines in various shapes.


Exercise 5.6: Classification of Triangles

This exercise involves classifying triangles based on their sides (equilateral, isosceles, scalene) and angles (acute-angled, obtuse-angled, right-angled). Students learn to identify and differentiate between these types.


Exercise 5.7: Understanding Quadrilaterals

Students are introduced to different types of quadrilaterals, such as squares, rectangles, parallelograms, and rhombuses. They learn to identify these shapes based on their properties.


Exercise 5.8: Polygons

This exercise helps students recognize and categorize polygons based on the number of sides. They learn about regular and irregular polygons and understand their properties.


Access NCERT Solutions for Class 6 Maths Chapter 5 – Understanding Elementary Shapes

Exercise 5.1

1. What is the disadvantage in comparing line segments by mere observation?

Ans: One of the main disadvantage in comparing the line segments by mere observation is that there will be high chances of miscalculation.


2. Why is it better to use a divider than a ruler, while measuring the length of a line segment?

Ans: We know that rulers are very thick. Hence, when we will measure the length, then we can misread the readings due to the thickness. Therefore, it is better to use a divider than a ruler.


3. Draw any line segment, say \[AB\]. Take any point \[C\] lying in between \[A\] and \[B\]. Measure the lengths of \[AB\], \[BC\] and \[AC\]. Is \[AB=AC+BC\]?

Ans: When we will draw any line segment $AB=7cm$ where $C$ is a point lying between $A$ and $B$ as shown in the figure below –


Line segment AB

We have $AC=3cm$ and

$BC=4cm$.

Therefore, $AB=AC+BC$

$\Rightarrow AB=3+4$

$\Rightarrow AB=7cm$.

Yes, $AB=AC+BC$.


4. If \[A,\ B,\ \text{C}\] are three points on a line such that \[AB=5cm\] , \[BC=3cm\] and \[AC=8cm\] , which one of them lies between the other two?

Ans: As, the sum of $AB$ and $BC$ is equal to the length of the line segment \[AC\]. i.e., $AC=AB+BC$

$\Rightarrow 8=5+3$.

Therefore, the point $B$ lies in between the line segment \[AC\].


5. Verify whether \[D\] is the mid-point of \[\overline{AG}\].


Line segment AG

Ans: From the figure we can observe that $AD=3cm$ and

$DG=3cm$. Therefore, $D$ is the mid-point.


6. If \[B\] is the mid-point of \[AC\] and \[C\] is the mid-point of \[BD\], where \[A\], \[B\], \[C\], \[D\] lie on a straight line, say why \[AB=CD\] ?

Ans:


Straight Line AD

As, given we have $B$ is the midpoint of $AC$.

$\Rightarrow AB=BC$

Similarly, $C$ is the midpoint of $BD$.

$\Rightarrow BC=CD$

From, the above conditions, we have $\Rightarrow AB=CD$. Hence, proved.


7. Draw five triangles and measure their sides. Check in each case, of the sum of the lengths of any two sides is always less than the third side.

Ans: No, from the given figures below we can conclude that the sum of two sides of a triangle can never be less than the third side of that triangle.


Five triangle


Exercise 5.2

1. What fraction of a clockwise revolution does the hour hand of a clock turn through, 

(i) when it goes from \[3\] to \[9\].

Ans: When the hour hand of a clock goes from $3$ to $9$, the number of divisions between them will be $6$, so the fraction will be $\frac{6}{12}=\frac{1}{2}$.


(ii) when it goes from \[4\] to \[7\].

Ans: When the hour hand of a clock goes from $4$ to $7$, the number of divisions between them will be $3$, so the fraction will be $\frac{3}{12}=\frac{1}{4}$.


(iii) when it goes from \[7\] to \[10\].

Ans: When the hour hand of a clock goes from $7$ to $10$, the number of divisions between them will be $3$, so the fraction will be $\frac{3}{12}=\frac{1}{4}$.


(iv) when it goes from \[12\] to \[9\].

Ans: When the hour hand of a clock goes from $12$ to $9$, the number of divisions between them will be $9$, so the fraction will be $\frac{9}{12}=\frac{3}{4}$.


(v) when it goes from \[1\] to \[10\].

Ans: When the hour hand of a clock goes from $1$ to $10$, the number of divisions between them will be $9$, so the fraction will be $\frac{9}{12}=\frac{3}{4}$.


(vi) when it goes from \[6\] to \[3\].

Ans: When the hour hand of a clock goes from $6$ to $3$, the number of divisions between them will be $9$, so the fraction will be $\frac{9}{12}=\frac{3}{4}$.


2. Where will the hand of a clock stop if it:

(a) starts at \[12\] and make \[\frac{1}{2}\] of a revolution, clockwise?

Ans: When the hand of a clock starts at $12$ and make $\frac{1}{2}$ of a revolution, clockwise then it will stop at $\frac{12}{2}=6$.


(b) starts at \[2\] and makes \[\frac{1}{2}\] of a revolution, clockwise?

Ans: When the hand of a clock starts at $2$ and make $\frac{1}{2}$ of a revolution, clockwise then it will stop at $2+\frac{12}{2}=8$.


(c) starts at \[5\] and makes \[\frac{1}{4}\] of a revolution, clockwise?

Ans: When the hand of a clock starts at $5$ and make $\frac{1}{4}$ of a revolution, clockwise then it will stop at $5+\frac{12}{4}=8$.


(d) starts at \[5\] and makes \[\frac{3}{4}\] of a revolution, clockwise?

Ans: When the hand of a clock starts at $5$ and make $\frac{3}{4}$ of a revolution, clockwise then it will stop at $5+12\times \frac{3}{4}=14$ i.e., at $2$ as one revolution is $=12$.


3. Which direction will you face if you start facing:

(a) East and make \[\frac{1}{2}\] of a revolution clockwise?

Ans:


Clockwise from east

When we will make $\frac{1}{2}$ of a revolution, clockwise from east, then we will face the west direction.


(b) East and make \[1\frac{1}{2}\] of a revolution clockwise?

Ans: When we will make $1\frac{1}{2}$ of a revolution, clockwise from east, then we will face the west direction.


(c) West and makes \[\frac{3}{4}\] of a revolution clockwise?

Ans:


Clockwise from west

When we will make $\frac{3}{4}$ of a revolution, clockwise from west, then we will face the north direction.


(d) South and make one full revolution?

Ans:


Revolution from south

When we will make a one full revolution from south, then we will face the south direction. There will be no need for mentioning clockwise or anti-clockwise because anyhow one full revolution will bring us back to the original direction.


4. What part of a revolution have you turned through if you stand facing –

(a) East and turn clockwise to face north?

Ans:


Clockwise from east to face north

When we will turn clockwise from east to face north, then the revolution will be $\frac{3}{4}$.


(b) South and turn clockwise to face east?

Ans:


Clockwise from south to face east

When we will turn clockwise from south to face east, then the revolution will be $\frac{3}{4}$.


(c) West and turn clockwise to face east?

Ans:


Hour hand of a clock from 3 to 6


When we will turn clockwise from west to face east, then the revolution will be $\frac{1}{2}$.


5. Find the number of right angles turned through by the hour hand of a clock 

(a) when it goes from \[3\] to \[6\].

Ans: When the hour hand of a clock goes from $3$ to $6$ then the number of right angles turned will be one.


Hour hand of a clock from 2 to 8


(b) when it goes from \[2\] to \[8\].

Ans: When the hour hand of a clock goes from $2$ to $8$ then the number of right angles turned will be two.


Hour hand of a clock from 5 to 11


(c) when it goes from \[5\] to \[11\].

Ans: When the hour hand of a clock goes from $5$ to $11$ then the number of right angles turned will be two.


Hour hand of a clock from 10 to 1


(d) when it goes from \[10\] to \[1\].

Ans: When the hour hand of a clock goes from $10$ to $1$ then the number of right angles turned will be one.


Hour hand of a clock from 12 to 9


(e) when it goes from \[12\] to \[9\].

Ans: When the hour hand of a clock goes from $12$ to $9$ then the number of right angles turned will be three.


Hour hand of a clock from 12 to 6


(f) when it goes from \[12\] to \[6\].

Ans: When the hour hand of a clock goes from $12$ to $6$ then the number of right angles turned will be two.


South to west in clockwise direction

6. How many right angles do you make if you start facing –

(a) South and turn clockwise to west?

Ans: When we start facing south and turn clockwise to west then the number of right angles turned will be one.


North to east in anti-clockwise direction

(b) North and turn anti-clockwise to east?

Ans: When we start facing north and turn anti-clockwise to east then the number of right angles turned will be three.


West to east direction

(c) West and turn to west?

Ans: When we start facing west and turn to west then the number of right angles turned will be four.


South to north direction

(d) South and turn to north?

Ans: When we start facing south and turn to north then the number of right angles turned will be two.


Clock pointing at 6 and 9

7. Where will the hour hand of a clock stop if it starts: 

(a) from \[6\] and turns through \[1\] right angle?

Ans: One right angle = One-fourth of complete rotation of a clock $\frac{1}{4}\times 12=3$

When the hour hand of a clock starts from $6$ and turns through $1$ right angle, then it will stop at $6+3=9$.


Clock pointing at 8 and 2

(b) from \[8\] and turns through \[2\] right angles?

Ans: One right angle = One-fourth of complete rotation of a clock $\frac{1}{4}\times 12=3$

When the hour hand of a clock starts from $8$ and turns through $2$ right angles, then it will stop at $8+3+3=14$ i.e., at $2$.


Clock pointing at 10 and 7

(c) from \[10\] and turns through \[3\] right angles?

Ans: One right angle = One-fourth of complete rotation of a clock $\frac{1}{4}\times 12=3$

When the hour hand of a clock starts from $10$ and turns through $3$ right angles, then it will stop at $10+3+3+3=19$ i.e., at 7$.


Clock pointing at 7

(d) from \[7\] and turns through \[2\] straight angles?

Ans: One Straight angle = 2 right angles

When the hour hand of a clock starts from $7$ and turns through $2$ straight angles, then it will stop at $7+6+6=19$ i.e., at 7.


Acute Angle


Exercise 5.3

1. Match the following:

(i) Straight angle     

(a) less than one-fourth a revolution 

(ii) Right angle 

(b) more than half a revolution

(iii) Acute angle 

(c) half of a revolution 

(iv) Obtuse angle  

(d) one-fourth a revolution

(v) Reflex angle 

(e) between \[\frac{1}{4}\] and \[\frac{1}{2}\] of a revolution 



(f) one complete revolution

 

Ans:

(i) Straight angle

(c) half of a revolution

(ii) Right angle

(d) one-fourth a revolution

(iii) Acute angle

(a) less than one-fourth a revolution

(iv) Obtuse angle

(e) between $\frac{1}{4}$ and $\frac{1}{2}$ of a revolution


(v) Reflex angle

(b) more than half a revolution


2. Classify each one of the following angles as right, straight, acute, obtuse or reflex:

(a) 

obtuse angle

Ans: It is an acute angle.


(b) 

right angle

Ans: It is an obtuse angle.


(c)

reflex angle

Ans: It is a right angle.


(d)

straight angle

Ans: It is a reflex angle.


(e)

acute angle

Ans: It is a straight angle.


(f) 

angle to find (acute)

Ans: It is an acute angle.


Exercise 5.4

1. What is the measure of –

(i) a right angle?

Ans: The measure of a right angle is $90{}^\circ $.


(ii) a straight angle?

Ans: The measure of a straight angle is $180{}^\circ $.


2. Say True or False:

(a) The measure of an acute angle \[<90{}^\circ \].

Ans: True.

As, we measure any acute angle, then it will always be less than a right angle.


(b) The measure of an obtuse angle \[<90{}^\circ \].

Ans: False.

When we measure an obtuse angle, then it will always be more than a right angle.


(c) The measure of a reflex angle \[>180{}^\circ \].

Ans: True.

A reflex angle is always more than the measure of a straight line.


(d) The measure of a complete revolution \[=360{}^\circ \].

Ans: True.

When we complete one revolution, it is measured as turn of two straight lines.


(e) If \[m\angle A=53{}^\circ \] and 

\[m\angle B=35{}^\circ \], then 

\[m\angle A>m\angle B\].

Ans: True.


3. Write down the measure of:

(a) some acute angles

Ans: As, an acute angle is measured as less than a right angle. Therefore, some of the acute angles will be $45{}^\circ $, $30{}^\circ $, and etc.


(b) some obtuse angles

Ans: As, an obtuse angle is measured as more than a right angle. Therefore, some of the obtuse angles will be $105{}^\circ $, $140{}^\circ $, and etc.


4. Measure the angles given below, using the protractor and write down the measure:

(a)

figure obtuse

Ans: After using the protractor, we can conclude that the given figure is an acute angle measured as $40{}^\circ $.


(b)

find angle right angle

Ans: After using the protractor, we can conclude that the given figure is an obtuse angle measured as $130{}^\circ $.


(c) 

find figure acute angle

Ans: After using the protractor, we can conclude that the given figure is a right angle measured as $90{}^\circ $.


(d)

find greater angle

Ans: After using the protractor, we can conclude that the given figure is an acute angle measured as $60{}^\circ $.


5. Which angle has a large measure? First estimate and then measure:


find angle great

Ans: After estimating we can conclude that the measure of angle $B$ is larger than the measure of angle $A$.

Measure of angle \[A=\]

The measure of angle $A$ is $40{}^\circ $.

Measure of angle \[B=\]

The measure of angle $B$ is $65{}^\circ $.


6. From these two angles which has larger measure? Estimate and then confirm by measuring them –


estimating angle

Ans: From the given figure we can estimate that the second angle has a larger measure than the first angle. After using the protractor, the measure of first angle is $45{}^\circ $ and the measure of second angle is $60{}^\circ $.


7. Fill in the blanks with acute, obtuse, right, or straight: 

(a) An angle whose measure is less than that of a right angle is __________.

Ans: An angle whose measure is less than that of a right angle is acute angle.


(b) An angle whose measure is greater than that of a right angle is __________. 

Ans: An angle whose measure is greater than that of a right angle is obtuse angle.


(c) An angle whose measure is the sum of the measures of two right angles is __________. 

Ans: An angle whose measure is the sum of the measures of two right angles is straight angle.


(d) When the sum of the measures of two angles is that of a right angle, then each one of them is __________. 

Ans: When the sum of the measures of two angles is that of a right angle, then each one of them is acute angle.


(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be ___________.

Ans: When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be obtuse angle.


8. Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).


find the in the clock

Ans: After estimating the measure of each angle shown in figure, we have –

(i) $30{}^\circ $

(ii) $120{}^\circ $

(iii) $60{}^\circ $

(iv) $150{}^\circ $


9. Find the angle measure between the hands of the clock in each figure:


angle 30

Ans: From the given figure, as the revolution is of $\frac{1}{4}$ from $9$ to $12$ hence, the measure of the angle in first figure will be of $90{}^\circ $, second figure has angle of measure $30{}^\circ $ as each division is equal and the third figure has angle of measure $180{}^\circ $ as the revolution is of $\frac{1}{2}$ which will form a straight line.


10. Investigate:

In the given figure, the angle measure \[30{}^\circ \]. Look at the same figure through a magnifying glass. Does the angle become larger? Does the size of the angle change?


measure nd classify angle

Ans: No, the size of the angle does not change and hence, remains same even after using the magnifying glass.


11. Measure and classify each angle:


angle table

Ans: The measure of each angle can be measured by the help of a protractor. Hence, the angles will be –


measure the angle

Exercise 5.5

1. Which of the following are models for perpendicular lines –

(a) The adjacent edges of a tabletop.

Ans: Yes, adjacent edges of a table top are perpendicular.


(b) The lines of a railway track.

Ans: No, the lines of a railway track are not perpendicular.


(c) The line segments forming the letter ‘\[L\]’.

Ans: Yes, the line segments forming the letter $L$ are perpendicular.


(d) The letter \[V\].

Ans: No, the letter $V$ is not perpendicular.


2. Let \[PQ\] be the perpendicular to the line segment \[XY\]. Let \[PQ\] and \[XY\] intersect in the point \[A\]. What is the measure of \[\angle PAY\].

Ans: As, $PQ$ and $XY$ are perpendicular line segments to each other and intersect at point $A$ can be shown in the figure below –


perpendicular to line

Therefore, the measure of $\angle PAY=90{}^\circ $.


3. There are two “set-squares” in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?

Ans: From the two “set-squares” in our box, we have one set-square as $30{}^\circ $, $60{}^\circ $, $90{}^\circ $ and another set-square as $45{}^\circ $, $45{}^\circ $, $90{}^\circ $. Therefore, the angle that is common is $90{}^\circ $.


4. Study the diagram. The line \[l\] is perpendicular to line \[m\].


nature of angle

(a) Is \[CE=EG\]?

Ans: As, $CE=2\ \text{units}$ and

$EG=2\ \text{units}$. Therefore, 

$CE=EG$.


(b) Does \[PE\] bisect \[CG\]?

Ans: From the given figure we can conclude that yes, $PE$ bisects $CG$.


(c) Identify any two-line segments for which \[PE\] is the perpendicular bisector.

Ans: Any two-line segments for which $PE$ is the perpendicular bisector are $DF$ and $CG$.

(d) Are these true? 

(i) \[AC>FG\]

Ans: Yes, it’s true. As, $AC=2\ \text{units}$ and

$FG=1\ \text{unit}$. Hence, $AC>FG$.


(ii) \[CD=GH\]

Ans: Yes, it’s true. As, both $CD$ and $GH$ are of $\text{1}\ \text{unit}$.


(iii) \[BC<EH\]

Ans: Yes, it’s true. As, $BC=1\ unit$ and

$EH=3\ \text{units}$. Hence, $BC<EH$.


Exercise 5.6

1. Name the types of following triangles: 

(a) Triangle with lengths of sides \[7cm\], \[8cm\] and \[9cm\].

Ans: As, all the three sides of the triangle have different lengths,

therefore, it is a scalene triangle.


(b) \[\Delta ABC\] with \[AB=8.7cm\],  \[AC=7cm\] and \[BC=6cm\].

Ans: As, all the three sides of the triangle have different lengths, therefore, it is a scalene triangle.


(c) \[\Delta PQR\] such that \[PQ=QR=PR=5cm\].

Ans: As, all the three sides of the triangle have same lengths, therefore, it is an equilateral triangle.


(d) \[\Delta DEF\] with \[m\angle D=90{}^\circ \].

Ans: Since, one of the angles of the triangle is $90{}^\circ $, therefore, it is a right-angled triangle.


(e) \[\Delta XYZ\] with \[m\angle Y=90{}^\circ \] and  \[XY=YZ\].

Ans: Since, one of the angles of the triangle is $90{}^\circ $, and two sides are of same length therefore, it is an isosceles right-angled triangle.


(f) \[\Delta LMN\] with \[m\angle L=30{}^\circ \], \[m\angle M=70{}^\circ \] and  \[m\angle N=80{}^\circ \].

Ans: Since, all the angles of the triangle are less than right angle, therefore, it is an acute triangle.


2. Match the following: Measure of Triangle Types of Triangle 

(i) \[3\] sides of equal length

(a) Scalene

(ii) \[2\] sides of equal length 

(b) Isosceles right angle 

(iii) All sides are of different length   

(c) Obtuse angle

(iv) \[3\] acute angles   

(d) Right angle 

(v) \[1\] right angle   

(e) Equilateral 

(vi) \[1\] obtuse angle    

(f) Acute angle

(vii) \[1\] right angle with two sides  

(g) Isosceles of equal length


Ans:

(i) \[3\] sides of equal length

(e) Equilateral 

(ii) \[2\] sides of equal length 

(g) Isosceles of equal length

(iii) All sides are of different length   

(a) Scalene

(iv) \[3\] acute angles   

(f) Acute angle

(v) \[1\] right angle   

(d) Right angle 

(vi) \[1\] obtuse angle    

(c) Obtuse angle

(vii) \[1\] right angle with two sides  

(b) Isosceles right angle


3. Name each of the following triangles in two different ways: (You may judge the nature of angle by observation).


match stck triangle

Ans: The triangles in two different ways will be as –

(a) Acute angled triangle and Isosceles triangle.

(b) Right-angled triangle and Scalene triangle.

(c) Obtuse-angled triangle and Isosceles triangle.

(d) Right-angled triangle and Isosceles triangle.

(e) Equilateral triangle and acute angled triangle.

(f) Obtuse-angled triangle and scalene triangle.


4. Can you make a triangle with

(a) \[3\] matchsticks – Triangle possible


match stik sq

(b) \[4\] matchsticks – Triangle not-possible


angle matchsticks

(c)  \[5\] matchsticks – Triangle Possible 

This is an acute angle triangle, and it is possible to make triangle with five matchsticks.


matchstick tri-06

(d) \[6\] matchsticks – Triangle Possible


polygon

Exercise 5.7

1. Say true or false: 

(a) Each angle of a rectangle is a right angle.

Ans:

True. Each side of a rectangle is a right angle.


(b) The opposite sides of a rectangle are equal in length.

Ans:

True. Opposite sides of a rectangle are always equal and parallel to each other.


(c) The diagonals of a square are perpendicular to one another.

Ans:

True. Square has diagonals that are bisecting each other at $90{}^\circ $.


(d) All the sides of a rhombus are of equal length.

Ans:

True. Rhombus has all sides of equal length.


(e) All the sides of a parallelogram are of equal length.

Ans:

False. Not all sides of a parallelogram are of equal length.


(f) The opposite sides of a trapezium are parallel.

Ans: False. Opposite sides of a trapezium are never equal.


2. Give reasons for the following: 

(a) A square can be thought of as a special rectangle.

Ans: As, opposite sides of a rectangle are equal, and all angles are $90{}^\circ $. Therefore, we can say square as a special rectangle with all sides of equal length and all angles as $90{}^\circ $.


  1. A rectangle can be thought of as a special parallelogram.

Ans: As, both rectangle and parallelogram have opposite sides equal and parallel to each other. Therefore, we can say that rectangle can be a special parallelogram.


(c) A square can be thought of as a special rhombus.

Ans: Because both square and rhombus has all sides of same length and also their diagonals bisect each other at $90{}^\circ $. Therefore, a square can be a special rhombus.


(d) Squares, rectangles, parallelograms are all quadrilateral.

Ans: A quadrilateral is a shape that has at least $4$ sides. Therefore, squares, rectangles, parallelograms are all types of quadrilaterals.


(e) Square is also a parallelogram.

Ans: Since, in parallelogram opposite sides are always equal and parallel to each other. Therefore, a square can also be a special parallelogram.


3. A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?

Ans: A square has its all sides in equal length and all angles are also equal. Therefore, a square is a regular quadrilateral.


Exercise 5.8

1. Examine whether the following are polygons. If anyone among these is not, say why?


name polygon

Ans: As, the figure in $(a)$ is not close, hence, it cannot be a polygon. Whereas figure $(b)$ is a closed shape, hence, it is a polygon. Similarly, in figure $(c)$ and $(d)$ as the shape is not enclosed by line segments, therefore, they are also not polygons.


2. Name each polygon:


Regular hexagon

Ans: The polygon in figure $(a)$ is a quadrilateral as it has four sides, in figure $(b)$ it is a triangle as it has three sides, in figure $(c)$ it is a pentagon as it has five sides and in figure $(d)$ it is a octagon as it has eight sides.


3. Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of the triangle you have drawn.

Ans: A rough sketch of a regular hexagon with connecting any three of its vertices and drawing a triangle will be as –


Regular octagon

So, we have joined three vertices $A$, $E$, and $F$. Therefore, the triangle formed is an isosceles triangle as two sides are equal.


4. Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.

Ans: A rough sketch of a regular octagon when a rectangle is drawn using any of its four vertices will be as –


Regular pentagon

Here, $CDGH$ is a rectangle.


5. A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.

Ans: A rough sketch of a pentagon with its diagonals will be as –


Cone

Here, $ABCDE$ is a pentagon which has diagonals as $AD$, $AC$, $BE$, and $BD$.


Overview of Deleted Syllabus for CBSE Class 6 Maths Understanding Elementary Shapes

Chapter

Dropped Topics

Understanding Elementary Shapes

5.10 - Three dimensional shapes.


Class 6 Maths Chapter 5: Exercises Breakdown

Exercise

Number of Questions

Exercise 5.1

1 Questions & Solutions

Exercise 5.2

7 Questions & Solutions

Exercise 5.3

2 Questions & Solutions

Exercise 5.4

11 Questions & Solutions

Exercise 5.5

4 Questions & Solutions

Exercise 5.6

4 Questions & Solutions

Exercise 5.7

4 Questions & Solutions

Exercise 5.8

5 Questions & Solutions


Conclusion

Chapter 5 of Class 6 Maths, "Understanding Elementary Shapes," provides students with a solid foundation in geometry. This chapter covers a wide range of topics, including measuring line segments, types of angles, classification of triangles and quadrilaterals, polygons, three-dimensional shapes, perpendicular lines, and symmetry. Each topic is designed to help students develop a comprehensive understanding of geometric concepts, which are essential for their further studies in mathematics.


In previous years' exams, Class 6th Maths Chapter 5 has been a significant part of the curriculum, with around 10-15 questions typically asked. 


Other Study Material for CBSE Class 6 Maths Chapter 5


Chapter-Specific NCERT Solutions for Class 6 Maths

Given below are the chapter-wise NCERT Solutions for Class 6 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.


FAQs on NCERT Solutions Class 6 Maths Chapter 5 Understanding Elementary Shapes

1. Why is it important to understand elementary shapes?

There are several reasons why understanding elementary shapes is important in Class 6 Maths and beyond:

  • Foundation for Geometry

  • Developing Spatial Reasoning

  • Real-World Applications

  • Problem-Solving Skills

  • Enhances Visualization

2. What are elementary shapes 2 D and 3 D in ch 5 class 6 maths?

Elementary shapes can be broadly categorized into two types: 2D (two-dimensional) and 3D (three-dimensional).


2D Shapes (Flat Shapes):

  • These shapes exist on a flat surface and have only two dimensions: length and width (or breadth).

  • Examples of some elementary 2D shapes include:

    • Squares: Four equal sides and four right angles.

    • Rectangles: Four straight sides with opposite sides equal in length and four right angles.

    • Circles: A perfectly round shape with all points at an equal distance from the center.

    • Triangles: Three straight sides and three angles that add up to 180 degrees. There are different types of triangles based on their side lengths (scalene, isosceles, equilateral) and angles (acute, right, obtuse).

    • Pentagons, Hexagons, Octagons (and other polygons): Shapes with straight sides and a specific number of sides (5, 6, 8 in these examples).

3D Shapes (Solid Shapes):

  • These shapes have three dimensions: length, width, and height (or depth).

  • They exist in the real world and have thickness or depth, unlike flat 2D shapes.

  • Examples of elementary 3D shapes include:

    • Cubes: Six square faces, all equal in size and with right angles between them.

    • Cuboids (Rectangular Prisms): Similar to cubes but with faces that may not all be squares.

    • Spheres: Perfectly round solid shapes with all points at an equal distance from the center.

    • Cones: One curved surface that tapers to a point (apex) at the base.

    • Cylinders: Two circular bases with a curved surface connecting them.

    • Pyramids: A base (usually a polygon) and triangular sides that meet at a point (apex).

3. What is shape in elementary?

In understanding elementary shapes, a shape refers to the form or outline of an object. Shapes are defined by their boundaries, which can be created by points, lines, and curves. These basic geometric figures are the foundation for more complex structures and are essential for understanding spatial relationships in mathematics.