# NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Written by Team Trustudies
Updated at 2021-05-07

## NCERT solutions for class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.1

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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

There may be chance of error due to improper viewing. So we use divider to compare the length of the given line segments.

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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

It is better to use a divider than a ruler, because the thickness of the ruler may cause difficulties in reading off her length. However divider gives up accurate measurement.

Q.3 Draw any line segment, say $$\overline {AB}$$. Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?
[Note: If A, B, C are any three points on a line such AC + CB = AB, then we can be sure that C lies between A and B]

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

There , A, B and C such that C lies between A and B and AB = 9 cm.
AC = 5 cm, CB = 4 cm.
$$\therefore$$ AC + CB = 5 cm + 4 cm = 9 cm.
And AB = 9 cm.
Hence, AB = AC + CB Proved.

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

AB + BC = 5 + 3 = 8 cm
And, AC = 8 cm
Hence, B lies between A and C.

Q.5 Verify, whether D is the mid point of$$\overline {AG} .$$

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

we have AG = 7 unit – 1 unit = 6 unit
AD = 4 unit – 1 unit = 3 unit
and DG = 7 unit – 4 unit = 3 unit
$$\therefore$$AG = AD + DG.
Hence, D is the mid point of AG.

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Guven B is the mid point of AC .
$$\therefore$$ AB = BC …(i)
Given, C is the mid-point of BD .
BC = CD .... (ii)
From Eq.(i) and (ii), We have
AB = CD

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(I) In first figure,
It is an equalatral triangle
Sum of two side = 5 + 5 = 10
10 > 5 Hence, the sum of any two sides of a triangle is greater than the third side.
(II) In second figure ,
Sum of two side = 5 + 5 = 10 , 5 + 3 = 8 , 5 + 3 = 8
$$\therefore$$ 10 > 3, 8 > 5 , 8 > 5
Hence, the sum of any two sides of a triangle is greater than the third side.
(III) In third figure,
Sum of two side = 6 + 10 = 16 , 8 + 10 = 18 , 6 + 8 = 14
$$\therefore$$ 16 > 8, 18 > 6, 14 > 10
Hence, the sum of any two sides of a triangle is greater than the third side.
(IV) In forth figure,
Sum of two side = 6 + 7 = 13 , 7 + 6 = 13 , 6 + 6 = 12
$$\therefore$$ 13 > 6, 13 > 6, 12 > 7
Hence, the sum of any two sides of a triangle is greater than the third side.
(IV) In fifth figure,
Sum of two side = 12 + 5 = 17 , 13 + 5 = 18 , 12 + 13 = 25
$$\therefore$$ 17 > 13, 18 > 12, 25 > 5
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 Understanding Elementary Shapes Exercise 5.2

Q.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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) 3 to 9
9 – 3 = 6 hour
In one revolution = 12 hour
No. of revolution = 6 / 12 = 1/2 revolution.
(b) 4 to 7
7 – 4 = 3 hour
In one revolution = 12 hour
No. of revolution = 3 / 12 = 1/4 revolution.
(c) 7 to 10
10 – 7 = 3 hour
In one revolution = 12 hour
No. of revolution = 3 / 12 = 1/4 revolution.
(d) 12 to 9 i.e., 0 to 9
9 – 0 = 9 hour
In one revolution = 12 hour
No. of revolution = 9 / 12 = 3/4 revolution.
(e) 1 to 10
10 – 1 = 9 hour
In one revolution = 12 hour
No. of revolution = 9 / 12 = 3/4 revolution.
(f) 6 to 3 i.e., 6 to 12 and then 12 to 3
6 to 12 = 12 – 6 = 6 hour and 12 to 3 = 0 to 3 = 3 – 0 = 3 hour
6 + 3 = 9 hour
In one revolution = 12 hour
No. of revolution = 9 / 12 = 3/4 revolution.

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) Starting from 12 and making 1/2 of a revolution,
In one revolution = 12 hour
$$\therefore$$ 1/2 revolution =( 1/2 ) × 12 = 6 hour
Then 12 + 6 I.e., 0 + 6 = 6
the clock hand stops at 6.
(b) Starting from 2 and making 1/2 of a revolution,
In one revolution = 12 hour
$$\therefore$$ 1/2 revolution =( 1/2 ) × 12 = 6 hour
Then 2 + 6 = 8
the clock hand stops at 8.
(c) Starting from 5 and making 1/4 of a revolution,
In one revolution = 12 hour
$$\therefore$$ 1/4 revolution =( 1/4 ) × 12 = 3 hour
Then 5 + 3 = 8
the clock hand stops at 8.
(d) Starting from 12 and making 3/4 of a revolution,
In one revolution = 12 hour
$$\therefore$$ 3/4 revolution =( 3/4 ) × 12 = 9 hour
Then 5 + 9 = 14 = 12 + 2 I.e., 0 +2 = 2
the clock hand stops at 2.

Q.3 Which direction will you face if you start facing
(a) east and make $$\frac{1}{2}$$ of a revolution clockwise? z
(b ) east and make$$1\frac{1}{2}$$ of a revolution clockwise? z
(c) west and make $$\frac{3}{4}$$ of a revolution anticlockwise?
(d) south and make one full revolution? (Should we specify clockwise or anticlockwise for this last question? Why not?)

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) west
(b) west
(c) north
(d) south
In case of revolving 1 complete revolution, either clockwise or anti-clockwise we will be back at the original position.

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) If we start from East and turn clockwise to face North, 3 /4 of a revolution is required.
(b) If we start from south and turn clockwise to face east, 3/4 of a revolution is required.
(c) If we start from west and turn clockwise to face east, 1/2 of a revolution is required.

Q.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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) 3 to 6 = 6 - 3 = 3 hour
In one revolution = 12 hour
No. of revolution = 3 / 12 = 1/4 revolution.
In one revolution = 4 right angle
$$\therefore$$ 1/4 revolution = (1\4) × 4 = 1 right angle
(b) 2 to 8 = 8 - 2 = 6 hour
In one revolution = 12 hour
No. of revolution = 6 / 12 = 1/2 revolution.
In one revolution = 4 right angle
$$\therefore$$ 1/2 revolution = (1\2) × 4 = 2 right angle
(c) 5 to 11 = 11 - 5 = 6 hour
In one revolution = 12 hour
No. of revolution = 6 / 12 = 1/2 revolution.
In one revolution = 4 right angle
$$\therefore$$ 1/2 revolution = (1\2) × 4 = 2 right angle
(d) 10 to 1 I.e., 10 to 13 = 13 - 10 = 3 hour
In one revolution = 12 hour
No. of revolution = 3 / 12 = 1/4 revolution.
In one revolution = 4 right angle
$$\therefore$$ 1/4 revolution = (1\4) × 4 = 1 right angle
(e) 12 to 9 I.e., 0 to 9 = 9 - 0 = 9 hour
In one revolution = 12 hour
No. of revolution = 9 / 12 = 3/4 revolution.
In one revolution = 4 right angle
$$\therefore$$ 3/4 revolution = (3\4) × 4 = 3 right angle
(f) 12 to 6 = 6 - 0 = 6 hour
In one revolution = 12 hour
No. of revolution = 6 / 12 = 1/2 revolution.
In one revolution = 4 right angle
$$\therefore$$ 1/2 revolution = (1\2) × 4 = 2 right angle

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) we know that in clock wise direction North to East one right angle , East to South

## NCERT solutions for class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.3

Q.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 $$\frac{1}{4}$$ and $$\frac{1}{4}$$ of a revolution
(f) One complete revolution

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(i) Straight angle $$\rightarrow$$ (c) Half of a revolution.
(ii) Right angle $$\rightarrow$$ (d) One-fourth of revolution.
(iii) Acute angle $$\rightarrow$$ (a) Less than one-fourth of a revolution.
(iv) Obtuse angle $$\rightarrow$$ (e) Between 14 and 12 of a revolution.
(v) Reflex angle $$\rightarrow$$ (f) One complete revolution, right, acute, obtuse or reflex.

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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) Acute angle
(b) Obtuse angle
(c) Right angle
(d) Reflex angle
(e) Straight angle
(f) Acute angle

## NCERT solutions for class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.4

Q.1 What is the measure of
(i) a right angle?
(ii) a straight angle

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(i) a right angle = 90°
(ii) a straight angle = 180°

Q.2 Say True or False:
(a) The measure of an acute angle < 90°
(b) The measure of an obtuse angle < 90°
(c) The measure of a reflex angle > 180°
(d) The measure of one complete revolution = 360°
(e) If m $$\angle$$ A = 53° and m $$\angle$$ B = 35°, then m $$\angle$$ A > m $$\angle$$B.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) True
(b) False
(c) True
(d) True
(e) True

Q.3 Write down the measures of
(a) some acute angles
(b) some obtuse angles
(give at least two examples of each)

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) 35°, 83° and 27° are acute angles.
(b) 112°, 130° and 95° are obtuse angles.

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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) 45°
(b) 125°
(c) 90°
(d) $$\angle$$1 = 60°, $$\angle$$2 = 90°, $$\angle$$3 = 125°

Q.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 Understanding Elementary Shapes

Measure of Angle A = 40°
Measure of Angle B = 60°.

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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

First angle = 45°
Second angle = 60°
Hence, second angle is greater

Q.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 ______

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(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°)
(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.

Q.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 Understanding Elementary Shapes

The measures of the angles shown in above figure are 40°, 130°, 65° and 135°

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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

The angle measure between the hands of the clock are 90°, 30° and 180°

Q.10 In the given figure, the angle measure 30°. 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 Understanding Elementary Shapes

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

Q.11 Measure and classify each angle:

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

## NCERT solutions for class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.5

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

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

Q.2 Let $$\overline {PQ}$$be the perpendicular to the line segment$$\overline {XY}$$. Let$$\overline {PQ}$$and $$\overline {XY}$$ intersect at in the point A. What is the measure of $$\angle$$PAY?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

$$\angle$$PAY = 90°

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

The measure angles of triangle (a) are : 30°, 60° and 90°.
The measure angles of triangle (b) are 45°, 45° and 90°.
Yes, they have a common angle of measure 90°.

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) Yes
(b) Yes,
(c)$$\overline{BG}$$ and $$\overline {DF}$$
(d) (i) True (ii) True (iii) True

## NCERT solutions for class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.6

Q.1 Name the types of following triangles:
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) $$\triangle$$ ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) $$\triangle$$PQR such that PQ = QR = PR = 5 cm.
(d) $$\triangle$$DEF with $$\angle$$D = 90°
(e) $$\triangle$$XYZ with $$\angle$$Y = 90° and XY = YZ.
(f) $$\triangle$$LMN with $$\angle$$L = 30°, ?M = 70° and ?N = 80°.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) Scalene triangle
(b) Scalene triangle
(c) Equilateral triangle
(d) Right angled triangle
(e) Right angled isosceles triangle
(f) Acute angled triangle

Q.2 Match the following:
Measures of Triangle Type of Triangle
(i) 3 sides of equal length $$\rightarrow$$ (a) Scalene (ii) 2 sides of equal length $$\rightarrow$$ (b) Isosceles right angled (iii) All sides are of different $$\rightarrow$$ (c) Obtuse angled (iv) 3 acute angles $$\rightarrow$$ (d) Right angled (v) 1 right angle $$\rightarrow$$ (e) Equilateral (vi) 1 obtuse angle $$\rightarrow$$ (f) Acute angled (vii) 1 right angle with two sides of equal length $$\rightarrow$$ (g) Isosceles

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(i) $$\rightarrow$$ Equilateral triangle
(ii) $$\rightarrow$$ Isosceles triangle
(iii) $$\rightarrow$$ Scalene triangle
(iv) $$\rightarrow$$ Acute angled triangle
(v) $$\rightarrow$$ Right angled triangle
(vi) $$\rightarrow$$ Obtuse angled triangle
(vii) $$\rightarrow$$ Isosceles right angled triangle

Q.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 Understanding Elementary Shapes

(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

Q.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 Understanding Elementary Shapes

(a) Yes, we can make an equilateral triangle with 3 matchsticks.
(b) No, we cannot make a triangle with 4 matchsticks.
(c) Yes, we can make an isosceles triangle with five matchsticks.
(d) Yes, we can make an equilateral triangle with 6 matchsticks.

## NCERT solutions for class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.7

Q.1 Say True or False:
(a) Each angle of a rectangle is a right angle.
(b) The opposite sides of a rectangle are equal in length.
(c) The diagonals of a square are perpendicular to one another.
(d) All the sides of a rhombus are of equal length.
(e) All the sides of a parallelogram are of equal length.
(f) The opposite sides of a trapezium are parallel.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) True
(b) True
(c) True
(d) True
(e) False
(f) False

Q.2 Give reasons for the following:
(a) A square can be thought of as a special rectangle.
(b) A rectangle can be thought of as a special parallelogram.
(c) A square can be thought of as a special rhombus.
(d) Squares, rectangles, parallelograms are all quadrilaterals.
(e) Square is also a parallelogram.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) A square has all the properties as that of rectangle. So, it is a special rectangle.
(b) A rectangle has the same properties as that of parallelogram. So, it is a special parallelogram.
(c) A square has the same properties as that of a rhombus. So, it is a special rhombus.
(d) Square, rectangles and parallelogram are all quadrilateral as they are all enclosed by four sides.

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Square is only the regular quadrilateral with equal sides and equal angles. Therefore, square is a regular quadrilateral.

## NCERT solutions for class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.8

Q.1 Examine whether the following are polygons. If any one among them is not, say why?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) The given figure is not closed. Therefore, it is not a polygon.
(b) The given figure is a polygon.
(c) The given figure is not a polygon because every polygon is enclosed with line segments.
(d) The given figure is not a polygon because it is enclosed by an arc and two line segments.

Q.2 Name each polygon.

Make two more examples of each of these.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(b) Triangle

(c) Pentagon

(d) hexagon

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

## NCERT solutions for class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.9

Q.1 Match the following:

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) $$\rightarrow$$ (ii)
(b) $$\rightarrow$$ (iv)
(c) $$\rightarrow$$ (v)
(d) $$\rightarrow$$ (iii)
(e) $$\rightarrow$$ (i)

Q.2 What shape is
(b) A brick?
(c) A match box?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

(a) cuboid
(b) cuboid
(c) cuboid
(d) cylinder
(e) sphere

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