**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.

**Contents**hide

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 **

**. 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

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 **

**.**

**Solutions:**

Since, it is clear from the figure that AD = DG = 3 units. Hence, D is the midpoint of** **

**Question 6. If B is the mid point of **

**and C is the mid point of
, where A, B, C, D lie on a straight line, say why AB = CD?**

**Solutions:**

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

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

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

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

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

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 360^{0}

(a) When hour hand goes from 3 to 9 clockwise, it will rotate by 2 right angles or 180^{0}

∴ Fraction = 180^{0} / 360^{0}

= 1 / 2

(b) When hour hand goes from 4 to 7 clockwise, it will rotate by 1 right angle or 90^{0}

∴ Fraction = 90^{0} / 360^{0}

= 1 / 4

(c) When hour hand goes from 7 to 10 clockwise, it will rotate by 1 right angle or 90^{0}

∴ Fraction = 90^{0} / 360^{0}

= 1 / 4

(d) When hour hand goes from 12 to 9 clockwise, it will rotate by 3 right angles or 270^{0}

∴ Fraction = 270^{0} / 360^{0}

= 3 / 4

(e) When hour hand of a clock goes from 1 to 10 clockwise, it will rotate by 3 right angles or 270^{0}

∴ Fraction = 270^{0} / 360^{0}

= 3 / 4

(f) When hour hand goes from 6 to 3 clockwise, it will rotate by 3 right angles or 270^{0}

∴ Fraction = 270^{0} / 360^{0}

= 3 / 4

**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 360^{0}

(a) When hour hand of a clock starts at 12 and makes 1 / 2 revolution clockwise, it will rotate by 180^{0}.

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

(b) When hour hand of a clock starts at 2 and makes 1 / 2 revolution clockwise, it will rotate by 180^{0}

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

(c) When hour hand of a clock starts at 5 and makes 1 / 4 revolution clockwise, it will rotate by 90^{0}

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

(d) When hour hand of a clock starts at 5 and makes 3 / 4 revolution clockwise, it will rotate by 270^{0}

Hence, hour hand of a clock will stop at 2

**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 360^{0} and two adjacent directions are at 90^{0} 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.

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

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

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

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 360^{0} and two adjacent directions are at 90^{0} 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

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

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

**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 360^{0} 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 90^{0} or 1 right angle

(b) If hour hand of a clock goes from 2 to 8, it revolves by 180^{0} or 2 right angles

(c) If hour hand of a clock goes from 5 to 11, it revolves by 180^{0} or 2 right angles

(d) If hour hand of a clock goes from 10 to 1, it revolves by 90^{0} or 1 right angle

(e) If hour hand of a clock goes from 12 to 9, it revolves by 270^{0} or 3 right angles

(f) If hour hand of a clock goes from 12 to 6, it revolves by 180^{0} or 2 right angles

**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 360^{0} and two adjacent directions are at 90^{0} away from each other.

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

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

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

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

**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 360^{0} 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

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

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

(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 **

**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 = 180^{0} or half of a revolution

Hence, (c) is correct answer

(ii) Right angle = 90^{0} or one-fourth of a revolution

Hence, (d) is correct answer

(iii) Acute angle = less than 90^{0} or less than one-fourth of a revolution

Hence, (a) is correct answer

(iv) Obtuse angle = more than 90^{0} but less than 180^{0} or between 1 / 4 and 1 / 2 of a revolution

Hence, (e) is correct answer

(v) Reflex angle = more than 180^{0} but less than 360^{0} 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:**

**Solutions:**

(i) The given angle is acute angle it measures less than 90^{0}

(ii) The given angle is obtuse angle as it measures more than 90^{0} but less than 180^{0}

(iii) The given angle is right angle as it measures 90^{0}

(iv) The given angle is reflex angle as it measures more than 180^{0} but less than 360^{0}

(v) The given angle is straight angle as it measures 180^{0}

(vi) The given angle is acute angle as it measures less than 90^{0}

**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 90^{0}

(ii) The measure of a straight angle is 180^{0}

**Question 2. Say True or False:**

**(a) The measure of an acute angle < 90 ^{0}**

**(b) The measure of an obtuse angle < 90 ^{0}**

**(c) The measure of a reflex angle > 180 ^{0}**

**(d) The measure of one complete revolution = 360 ^{0}**

**(e) If m ∠A = 53 ^{0} and m ∠B = 35^{0}, then m ∠A > m ∠B.**

**Solutions:**

**(a) **True, the measure of an acute angle is less than 90^{0}

(b) False, the measure of an obtuse angle is more than 90^{0} but less than 180^{0}

(c) True, the measure of a reflex angle is more than 180^{0}

(d) True, the measure of one complete revolution is 360^{0}

(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 50^{0}, 65^{0}

(b) The measures of obtuse angle are 110^{0}, 175^{0}

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

**Solutions:**

**(a) **The measure of an angle is 45^{0}

(b) The measure of an angle is 120^{0}

(c) The measure of an angle is 90^{0}

(d) The measures of an angles are 60^{0}, 90^{0} and 130^{0}

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

**Measure of Angle A =**

**Measure of Angle B =**

**Solutions:**

The measure of angle A is 40

^{0}

The measure of angle B is 68

^{0}

∠B has a large measure than ∠A

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

**Solutions:**

The measures of these angles are 45^{0} and 55^{0}. 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 180^{0})

(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).**

**Solutions:**

The measures of the angles shown in above figure are 40^{0}, 130^{0}, 65^{0} and 135^{0}

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

**Solutions:**

The angle measure between the hands of the clock are 90^{0}, 30^{0} and 180^{0}

**Question 10. Investigate**

**In the given figure, the angle measure 30 ^{0}. Look at the same figure through a magnifying glass. Does the angle becomes larger? Does the size of the angle change?**

**Solutions:**

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

**Question 11. Measure and classify each angle:**

**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 **

**be the perpendicular to the line segment
. Let
and
intersect in the point A. What is the measure of ∠PAY?**

**Solutions:**

From the figure it is clear that the measure of ∠PAY is 90^{0}

**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 30^{0}, 60^{0} and 90^{0}

The other set square has a measure of angles 45^{0}, 45^{0} and 90^{0}

Yes, the angle of measure 90^{0} is common in between them

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

**(a) Is CE = EG?**

**(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)

(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)**

**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**

**Solutions:**

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

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

The above triangle is an isosceles triangle

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

The above triangle is an equilateral triangle