NCERT Solutions For Class 6 Maths Chapter 5: Understanding Elementary Shapes ( New Syllabus)

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes are available here so that students can learn better and more effectively. Study Circle provides online learning materials for almost all classes like notes, question papers, example problems etc.

This helps all students in every way, which students can use in the form of worksheets for good exam preparation. The NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes are provided here to help the students in their exam preparation.

Practicing these solved problems of NCERT Solutions for Class 6 Maths Chapter 5 will help students to understand the techniques to solve different types of questions. All the solutions in this article are based on the new NCERT Solutions.

NCERT Solutions For Class 6 Maths Chapter 5 : Exercise 5.1

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

Solutions:

By mere observation we can’t compare the line segments with slight difference in their length. We can’t say which line segment is of greater length. Hence, the chances of errors due to improper viewing are higher.

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

Solutions:

While using a ruler, chances of error occur due to thickness of the ruler and angular viewing. Hence, using divider accurate measurement is possible.

Question 3. Draw any line segment, say NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1 - 1

. Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?

Solutions:

Since given that point C lie in between A and B. Hence, all points are lying on same line segment
NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1 - 2

. Therefore for every situation in which point C is lying in between A and B we may say that

AB = AC + CB

For example:

AB is a line segment of length 7 cm and C is a point between A and B such that AC = 3 cm and CB = 4 cm.

Hence, AC + CB = 7 cm

Since, AB = 7 cm

∴ AB = AC + CB is verified.

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

Solutions:

Given AB = 5 cm

BC = 3 cm

AC = 8 cm

Now, it is clear that AC = AB + BC

Hence, point B lies between A and C.

Question 5. Verify whether D is the mid point of NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1 - 3

.

NCERT Solutions for Class 6 Maths Chapter 5

Solutions:

Since, it is clear from the figure that AD = DG = 3 units. Hence, D is the midpoint of NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1 - 5

Question 6. If B is the mid point of NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1 - 6

 and C is the mid point of NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1 - 7
, where A, B, C, D lie on a straight line, say why AB = CD?

Solutions:

NCERT Solutions for Class 6 Maths Chapter 5

Given

B is the midpoint of AC. Hence, AB = BC (1)

C is the midpoint of BD. Hence, BC = CD (2)

From (1) and (2)

AB = CD is verified

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

Solutions:

Case 1. In triangle ABC

NCERT Solutions for Class 6 Maths Chapter 5

AB= 2.5 cm

BC = 4.8 cm and

AC = 5.2 cm

AB + BC = 2.5 cm + 4.8 cm

= 7.3 cm

As 7.3 > 5.2

∴ AB + BC > AC

Hence, the sum of any two sides of a triangle is greater than the third side.

Case 2. In triangle PQR

NCERT Solutions for Class 6 Maths Chapter 5

PQ = 2 cm

QR = 2.5 cm

PR = 3.5 cm

PQ + QR = 2 cm + 2.5 cm

= 4.5 cm

As 4.5 > 3.5

∴ PQ + QR > PR

Hence, the sum of any two sides of a triangle is greater than the third side.

Case 3. In triangle XYZ

NCERT Solutions for Class 6 Maths Chapter 5

XY = 5 cm

YZ = 3 cm

ZX = 6.8 cm

XY + YZ = 5 cm + 3 cm

= 8 cm

As 8 > 6.8

∴ XY + YZ > ZX

Hence, the sum of any two sides of a triangle is greater than the third side.

Case 4. In triangle MNS

NCERT Solutions for Class 6 Maths Chapter 5

MN = 2.7 cm

NS = 4 cm

MS = 4.7 cm

MN + NS = 2.7 cm + 4 cm

6.7 cm

As 6.7 > 4.7

∴ MN + NS > MS

Hence, the sum of any two sides of a triangle is greater than the third side.

Case 5. In triangle KLM

NCERT Solutions for Class 6 Maths Chapter 5

KL = 3.5 cm

LM = 3.5 cm

KM = 3.5 cm

KL + LM = 3.5 cm + 3.5 cm

= 7 cm

As 7 cm > 3.5 cm

∴ KL + LM > KM

Hence, the sum of any two sides of a triangle is greater than the third side.

Therefore, we conclude that the sum of any two sides of a triangle is always greater than the third side.

NCERT Solutions for Class 6 Maths Chapter 5 

Exercise 5.2

Question 1. What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from

(a) 3 to 9

(b) 4 to 7

(c) 7 to 10

(d) 12 to 9

(e) 1 to 10

(f) 6 to 3

Solutions:

We know that in one complete clockwise revolution, hour hand will rotate by 3600

(a) When hour hand goes from 3 to 9 clockwise, it will rotate by 2 right angles or 1800

∴ Fraction = 1800 / 3600

= 1 / 2

NCERT Solutions for Class 6 Maths Chapter 5

(b) When hour hand goes from 4 to 7 clockwise, it will rotate by 1 right angle or 900

∴ Fraction = 900 / 3600

= 1 / 4

NCERT Solutions for Class 6 Maths Chapter 5

(c) When hour hand goes from 7 to 10 clockwise, it will rotate by 1 right angle or 900

∴ Fraction = 900 / 3600

= 1 / 4

NCERT Solutions for Class 6 Maths Chapter 5

(d) When hour hand goes from 12 to 9 clockwise, it will rotate by 3 right angles or 2700

∴ Fraction = 2700 / 3600

= 3 / 4

 

NCERT Solutions for Class 6 Maths Chapter 5

(e) When hour hand of a clock goes from 1 to 10 clockwise, it will rotate by 3 right angles or 2700

∴ Fraction = 2700 / 3600

= 3 / 4

NCERT Solutions for Class 6 Maths Chapter 5

(f) When hour hand goes from 6 to 3 clockwise, it will rotate by 3 right angles or 2700

∴ Fraction = 2700 / 3600

= 3 / 4

NCERT Solutions for Class 6 Maths Chapter 5

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

(a) starts at 12 and makes 1 / 2 of a revolution, clockwise?

(b) starts at 2 and makes 1 / 2 of a revolution, clockwise?

(c) starts at 5 and makes 1 / 4 of a revolution, clockwise?

(d) starts at 5 and makes 3 / 4 of a revolution, clockwise?

Solutions:

We know that one complete clockwise revolution, hour hand will rotate by 3600

(a) When hour hand of a clock starts at 12 and makes 1 / 2 revolution clockwise, it will rotate by 1800.

Hence, the hour hand of a clock will stop at 6.

NCERT Solutions for Class 6 Maths Chapter 5

(b) When hour hand of a clock starts at 2 and makes 1 / 2 revolution clockwise, it will rotate by 1800

Hence, the hour hand of a clock will stop at 8.

NCERT Solutions for Class 6 Maths Chapter 5

(c) When hour hand of a clock starts at 5 and makes 1 / 4 revolution clockwise, it will rotate by 900

Hence, hour hand of a clock will stop at 8.

NCERT Solutions for Class 6 Maths Chapter 5

(d) When hour hand of a clock starts at 5 and makes 3 / 4 revolution clockwise, it will rotate by 2700

Hence, hour hand of a clock will stop at 2

NCERT Solutions for Class 6 Maths Chapter 5

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

(a) east and make 1 / 2 of a revolution clockwise?

(b) east and make 1 ½ of a revolution clockwise?

(c) west and make 3 / 4 of a revolution anti – clockwise?

(d) south and make one full revolution?

(should we specify clockwise or anti – clockwise for this last question? Why not?)

Solutions:

Revolving one complete round in clockwise or in anti – clockwise direction we will revolve by 3600 and two adjacent directions are at 900 or 1 / 4 of a complete revolution away from each other.

(a) If we start facing towards East and make 1 / 2 of a revolution clockwise, we will face towards West direction.

 

NCERT Solutions for Class 6 Maths Chapter 5

(b) If we start facing towards East and make 1 ½ of a revolution clockwise, we will face towards West direction

 

NCERT Solutions for Class 6 Maths Chapter 5

(c) If we start facing towards West and make 3 / 4 of a revolution anti – clockwise, we will face towards North direction

 

NCERT Solutions for Class 6 Maths Chapter 5

(d) If we start facing South and make one full revolution, again we will face the South direction.

 

NCERT Solutions for Class 6 Maths Chapter 5

In case of revolving 1 complete revolution, either clockwise or anti-clockwise we will be back at the original position.

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

(a) east and turn clockwise to face north?

(b) south and turn clockwise to face east

(c) west and turn clockwise to face east?

Solutions:

By revolving one complete revolution either in clockwise or in anti-clockwise direction, we will revolve by 3600 and two adjacent directions are at 900 or 1 / 4 of a complete revolution away from each other

(a) If we start facing towards East and turn clockwise to face North, we have to make 3 / 4 of a revolution

NCERT Solutions for Class 6 Maths Chapter 5

(b) If we start facing towards South and turn clockwise to face East, we have to make 3 / 4 of a revolution

NCERT Solutions for Class 6 Maths Chapter 5

 

(c) If we start facing towards West and turn clockwise to face East, we have to make 1 / 2 of a revolution

NCERT Solutions for Class 6 Maths Chapter 5

Question 5. Find the number of right angles turned through by the hour hand of a clock when it goes from

(a) 3 to 6

(b) 2 to 8

(c) 5 to 11

(d) 10 to 1

(e) 12 to 9

(f) 12 to 6

Solutions:

The hour hand of a clock revolves by 3600 or it covers 4 right angles in one complete revolution

(a) If hour hand of a clock goes from 3 to 6, it revolves by 900 or 1 right angle

NCERT Solutions for Class 6 Maths Chapter 5

(b) If hour hand of a clock goes from 2 to 8, it revolves by 1800 or 2 right angles

 

NCERT Solutions for Class 6 Maths Chapter 5

(c) If hour hand of a clock goes from 5 to 11, it revolves by 1800 or 2 right angles

NCERT Solutions for Class 6 Maths Chapter 5

(d) If hour hand of a clock goes from 10 to 1, it revolves by 900 or 1 right angle

NCERT Solutions for Class 6 Maths Chapter 5

(e) If hour hand of a clock goes from 12 to 9, it revolves by 2700 or 3 right angles

 

NCERT Solutions for Class 6 Maths Chapter 5

(f) If hour hand of a clock goes from 12 to 6, it revolves by 1800 or 2 right angles

 

NCERT Solutions for Class 6 Maths Chapter 5

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

(a) south and turn clockwise to west?

(b) north and turn anti – clockwise to east?

(c) west and turn to west?

(d) south and turn to north?

Solutions:

By revolving one complete round in either clockwise or anti-clockwise direction, we will revolve by 3600 and two adjacent directions are at 900 away from each other.

(a) If we start facing towards South and turn clockwise to West, we have to make one right angle

NCERT Solutions For Class 6 Maths Chapter 5

 

(b) If we start facing towards North and turn anti-clockwise to East, we have to make 3 right angles

NCERT Solutions For Class 6 Maths Chapter 5

(c) If we start facing towards West and turn to West, we have to make one complete round or 4 right angles

NCERT Solutions For Class 6 Maths Chapter 5

(d) If we start facing towards South and turn to North, we have to make 2 right angles

NCERT Solutions For Class 6 Maths Chapter 5

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

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

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

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

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

Solutions:

We know that in 1 complete revolution in either clockwise or anticlockwise direction, hour hand of a clock will rotate by 3600 or 4 right angles

(a) If hour hand of a clock starts from 6 and turns through 1 right angle, it will stop at 9

NCERT Solutions For Class 6 Maths Chapter 5

(b) If hour hand of a clock starts from 8 and turns through 2 right angles, it will stop at 2

NCERT Solutions For Class 6 Maths Chapter 5

(c) If hour hand of a clock starts from 10 and turns through 3 right angles, it will stop at 7

NCERT Solutions For Class 6 Maths Chapter 5

(d) If hour hand of a clock starts from 7 and turns through 2 straight angles, it will stop at 7

NCERT Solutions For Class 6 Maths Chapter 5

NCERT Solutions For Class 6 Maths Chapter 5  

Exercise 5.3

Question 1. Match the following:

(i) Straight angle (a) Less than one-fourth of 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 of a revolution

(v) Reflex angle (e) Between 1 / 4 and 1 / 2 of a revolution

(f) One complete revolution

Solutions:

(i) Straight angle = 1800 or half of a revolution

Hence, (c) is correct answer

(ii) Right angle = 900 or one-fourth of a revolution

Hence, (d) is correct answer

(iii) Acute angle = less than 900 or less than one-fourth of a revolution

Hence, (a) is correct answer

(iv) Obtuse angle = more than 900 but less than 1800 or between 1 / 4 and 1 / 2 of a revolution

Hence, (e) is correct answer

(v) Reflex angle = more than 1800 but less than 3600 or more than half a revolution

Hence, (b) is correct answer

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

NCERT Solutions For Class 6 Maths Chapter 5

Solutions:

(i) The given angle is acute angle it measures less than 900

(ii) The given angle is obtuse angle as it measures more than 900 but less than 1800

(iii) The given angle is right angle as it measures 900

(iv) The given angle is reflex angle as it measures more than 1800 but less than 3600

(v) The given angle is straight angle as it measures 1800

(vi) The given angle is acute angle as it measures less than 900

NCERT Solutions For Class 6 Maths Chapter 5

Exercise 5.4

Question 1. What is the measure of

(i) a right angle

(ii) a straight angle

Solutions:

(i) The measure of a right angle is 900

(ii) The measure of a straight angle is 1800

Question 2. Say True or False:

(a) The measure of an acute angle < 900

(b) The measure of an obtuse angle < 900

(c) The measure of a reflex angle > 1800

(d) The measure of one complete revolution = 3600

(e) If m ∠A = 530 and m ∠B = 350, then m ∠A > m ∠B.

Solutions:

(a) True, the measure of an acute angle is less than 900

(b) False, the measure of an obtuse angle is more than 900 but less than 1800

(c) True, the measure of a reflex angle is more than 1800

(d) True, the measure of one complete revolution is 3600

(e) True, ∠A is greater than ∠B

Question 3. Write down the measures of

(a) some acute angles

(b) some obtuse angles

(give at least two examples of each)

Solutions:

(a) The measures of an acute angle are 500, 650

(b) The measures of obtuse angle are 1100, 1750

Question 4. Measures the angles given below using the protractor and write down the measure.

NCERT Solutions For Class 6 Maths Chapter 5

Solutions:

(a) The measure of an angle is 450

(b) The measure of an angle is 1200

(c) The measure of an angle is 900

(d) The measures of an angles are 600, 900 and 1300

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

Measure of Angle A =

Measure of Angle B =

NCERT Solutions For Class 6 Maths Chapter 5

Solutions:
The measure of angle A is 400
The measure of angle B is 680
∠B has a large measure than ∠A
6. From these two angles which has larger measure? Estimate and then confirm by measuring them.NCERT Solutions For Class 6 Maths Chapter 5
Solutions:

The measures of these angles are 450 and 550. Hence, angle shown in second figure is greater.

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 _____

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

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

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

(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 ______

Solutions:

(a) 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 obtuse angle (but less than 1800)

(c) 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 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 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).

NCERT Solutions For Class 6 Maths Chapter 5

Solutions:

The measures of the angles shown in above figure are 400, 1300, 650 and 1350

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

NCERT Solutions For Class 6 Maths Chapter 5

Solutions:

The angle measure between the hands of the clock are 900, 300 and 1800

Question 10. Investigate

In the given figure, the angle measure 300. Look at the same figure through a magnifying glass. Does the angle becomes larger? Does the size of the angle change?

NCERT Solutions For Class 6 Maths Chapter 5

Solutions:

The measure of an angle will not change by viewing through a magnifying glass

Question 11. Measure and classify each angle:

NCERT Solutions For Class 6 Maths Chapter 5

NCERT Solutions For Class 6 Maths Chapter 5

NCERT Solutions For Class 6 Maths Chapter 5

Exercise 5.5

Question 1. Which of the following are models for perpendicular lines:

(a) The adjacent edges of a table top.

(b) The lines of a railway track.

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

(d) The letter V.

Solutions:

(a) The adjacent edges of a table top are perpendicular to each other.

(b) The lines of a railway track are parallel to each other.

(c) The line segments forming the letter ‘L’ are perpendicular to each other

(d) The sides of letter V are inclined forming an acute angle.

Therefore (a) and (c) are models for perpendicular lines.

Question 2. Let NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.5 - 1

 be the perpendicular to the line segment NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.5 - 2
. Let NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.5 - 3
 and NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.5 - 4
 intersect in the point A. What is the measure of ∠PAY?

Solutions:

NCERT Solutions for Class 6 Maths Chapter 5

From the figure it is clear that the measure of ∠PAY is 900

Question 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?

Solutions:

The measure of angles in one set square are 300, 600 and 900

The other set square has a measure of angles 450, 450 and 900

Yes, the angle of measure 900 is common in between them

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

(a) Is CE = EG?

NCERT Solutions for Class 6 Maths Chapter 5

 

(b) Does PE bisect CG?

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

(d) Are these true?

(i) AC > FG

(ii) CD = GH

(iii) BC < EH.

Solutions:

(a) Yes, since, CE = 2 units and EG = 2 units respectively

(b) Yes. Since, CE = EG as both are of 2 units. Hence PE bisect CG

(c) NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.5 - 7

and NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.5 - 8
are the line segments for which PE is the perpendicular bisector

(d) (i) True. Since AC = 2 units and FG = 1 unit

∴ AC > FG

(ii) True because both are of 1 unit

(iii) True. Since, BC = 1 unit and EH = 3 units

∴ BC < EH

Exercise 5.6

 

Question 1. Name the types of following triangles:

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

(b) ∆ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.

(c) ∆PQR such that PQ = QR = PR = 5 cm.

(d) ∆DEF with ∠D = 90°

(e) ∆XYZ with ∠Y = 90° and XY = YZ.

(f) ∆LMN with ∠L = 30°, ∠M = 70° and ∠N = 80°.

Solutions:

(a) Scalene triangle

(b) Scalene triangle

(c) Equilateral triangle

(d) Right angled triangle

(e) Right angled isosceles triangle

(f) Acute angled triangle

Question 2. Match the following:

Measures of Triangle Type of Triangle

(i) 3 sides of equal length                                                                                 (a) Scalene

(ii) 2 sides of equal length                                                                                (b) Isosceles right angled

(iii) All sides are of different length                                                             (c) Obtuse angled

(iv) 3 acute angles                                                                                                (d) Right angled

(v) 1 right angle                                                                                                      (e) Equilateral

(vi) 1 obtuse angle                                                                                                  (f) Acute angled

(vii) 1 right angle with two sides of equal length                                       (g) Isosceles

Solutions:

(i) Equilateral triangle

(ii) Isosceles triangle

(iii) Scalene triangle

(iv) Acute angled triangle

(v) Right angled triangle

(vi) Obtuse angled triangle

(vii) Isosceles right angled triangle

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

NCERT Solutions for Class 6 Maths Chapter 5

Solutions:

(i) Acute angled and isosceles triangle

(ii) Right angled and scalene triangle

(iii) Obtuse angled and isosceles triangle

(iv) Right angled and isosceles triangle

(v) Equilateral and acute angled triangle

(vi) Obtuse angled and scalene triangle

Question 4. Try to construct triangles using match sticks. Some are shown here. Can you make a triangle with

(a) 3 matchsticks?

(b) 4 matchsticks?

(c) 5 matchsticks?

(d) 6 matchsticks?

(Remember you have to use all the available matchsticks in each case)

Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it

 

NCERT Solutions for Class 6 Maths Chapter 5

Solutions:

(a) By using three match sticks we may make a triangle as shown below

 

NCERT Solutions for Class 6 Maths Chapter 5

The above triangle is an equilateral triangle

(b) By using 4 match sticks we cannot make a triangle, since we know that sum of the lengths of any two sides of a triangle is always greater than the third side.

(c) By using 5 match sticks we may make a triangle as shown below

NCERT Solutions for Class 6 Maths Chapter

The above triangle is an isosceles triangle

(d) By using 6 match sticks we may make a triangle as shown below

 

NCERT Solutions for Class 6 Maths Chapter 5

The above triangle is an equilateral triangle

 

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