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

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NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes by Swiflearn are by far the best and most reliable NCERT Solutions that you can find on the internet. These NCERT Solutions for Class 6 Maths Chapter 5 are designed as per the CBSE Class 6 Maths Syllabus. These NCERT Solutions will surely make your learning convenient & fun. Students can also Download FREE PDF of NCERT Solutions Class 6 Chapter 5.

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NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 5.1

 

NCERT 6th Maths Chapter 5 Exercise 5.1 1

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

 

Solution:
This will lead us to miscalculations, which we don’t want.

 

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

 

Solution:
The thickness of ruler may cause inconvenience, while measuring the line segment.

 

Question 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 + CB?
[Note: If A, B, C are any three points on a line, such that AC + CB = AB,
then we can be sure that C lies between A and B.]

 

Solution:
As it is given in the question that C lies between the points A and B, AC + CB = AB

Measure AC, CB and AB.
AC = 6 cm
CB = 2 cm
AB = 8 cm
Thus, AC + CB = AB

 

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

 

Solution:

As, it can be seen that AC = AB + BC, it can be said that B lies between A and C.

 

Question 5:
Verify whether D is the mid-point of AG .

Solution:
From the given figure we can see that, AD = 3 units and DG = 3 units, so we can say that D is the mid-point.

 

Question 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?

 

Solution:
(i)

The sum of the two sides is always greater than the third side.

(ii)

The sum of the two sides is always greater than the third side.

(iii)

The sum of the two sides is always greater than the third side.

(iv)

The sum of the two sides is always greater than the third side.

(v)

The sum of the two sides is always greater than the third side.

NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 5.2

 

NCERT 6th Maths Chapter 5 Exercise 5.2 1

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

 

Solution:
The fraction of revolution that hour hand turn of a clock turn in each case is as follows,

 

Question 2:
Where will the hand of a clock stop if it:
(a) Starts at 12 and make 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 1/3 of a revolution, clockwise?

 

Solution:
(a) At 6 o’clock.
(b) At 8 o’clock.
(c) At 8 o’clock.
(d) At 2 o’clock.

 

 

 

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 1/2of a revolution clockwise?
(c) West and make 3/4 of a revolution, clockwise?
(d) South and make one full revolution?
(Should we specify clockwise or anti-clockwise for this last question? Why
not?)

 

Solution:

The directions are as follows,
(a) West

(b) West

(c) North

(d) South ( clockwise or anti-clockwise doesn’t matter in this case since full revolution will make bring us back to original in both cases).

 

 

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?

 

Solution:
The amount of revolution in each case is as followed,
(a)3/4

(b)3/4

(c)1/52

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

 

Solution:
The number of right angles turned in each case is,
(a) One right angle (b) Two right angles
(c) Two right angles (d) One right angle

(e) Three right angles (f) Two 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?

 

Solution:
The number of right angles turned in each case is,
(a) One right angle (b) Three right angles
(c) Four right angles (d) Two 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?

 

Solution:
The hour hand will be at,
(a) At 9 (b) At 2 (c) At 7 (d) At 7

NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 5.3

 

NCERT 6th Maths Chapter 5 Exercise 5.3 1

Question 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 and of a revolution
(f) One complete revolution

 

Solution:
(i) – (c)
(ii) – (d)
(iii) – (a)
(iv) – (e)
(v) – (b)

 

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

 

Solution:
The angles are named as follows,
(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 Ex 5.4

 

NCERT 6th Maths Chapter 5 Exercise 5.4 1

Question 1:
What is the measure of (i) a right angle? (ii) a straight angle?

 

Solution:
The measure of a right angle is 900
and that of a straight angle is 1800

 

.
Question 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 on complete revolution = 360 .
(e) If m A = 53 and mB = 35 ,then m A > mB.

 

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

 

Question 3:
Write down the measure of:
(a) Some acute angles (b) Some obtuse angles
(Give at least two examples of each)

 

Solution:
(a) 30 , 45
(b) 130 , 169

 

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

Solution:
The measure of the angles is,
(a) 45 (b) 120 (c) 90 (d)1= 60 ,2= 95 , 3= 135

 

 

Question 5:
Which angle has a large measure? First estimate and then measure:
Measure of angle A =
Measure of angle B =

Solution:
By observation we can see that measure of angle B is greater.
A = 45
B = 60

 

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

 

Solution:
By observation we can see that (b) has a bigger angle measure,
Measure of angle A = 450
Measure of angle B = 600
Hence, confirmed.

 

Question 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 ________.

 

Solution:
(a) Acute angle
(b) Obtuse angle
(c) Straight angle
(d) Acute angle
(e) Obtuse angle

 

Question 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).

Solution:

(i) 30 (ii) 120 (iii) 60 (iv) 150

 

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

Solution:
(a) 900
(b) 300
(c) 1800

 

Question 10:
Investigate:
In the given figure, the angle measure 300. Look at the same figure through
a magnifying glass. Does the angle become larger? Does the size of the
angle change?

Solution:
No, the measure of the angle will be same.

 

Question 11:

Measure and classify each angle:

 

Solution:

NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 5.5

 

NCERT 6th Maths Chapter 5 Exercise 5.5 1

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.

 

Solution:
The models which show perpendicular lines are,
(a) Perpendicular
(b) Not perpendicular
(c) Perpendicular
(d) Not perpendicular

 

Question 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 PAY.

 

Solution:
As we can see in the question, it is given that PQ is perpendicular to XY and thus,

Thus,PAY = 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?

 

Solution:

 

Question 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

 

Solution:
(a) Yes.
(b) Yes.
(c) PE is the perpendicular bisector for CG and BH
(d) (i) True (ii) True (iii) True

NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 5.6

 

NCERT 6th Maths Chapter 5 Exercise 5.6 1

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 mD = 900
(e)XYZ with mY = 900 and XY = YZ
(f)LMN with mL = 300, m M = 700nand mN = 800
.
Solution:
The type of the triangle in each case is,
(a) Scalene triangle
(b) Scalene triangle
(c) Equilateral triangle
(d) Right-angled triangle
(e) Isosceles right-angled triangle
(f) Acute-angled triangle

 

Question 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

 

Solution:
(i) → (e)
(ii) → (g)
(iii) → (a)
(iv) → (f)
(v) → (d)
(vi) → (c)
(vii) → (b)

 

Question 3:

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

 

Solution:
(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

 

Question 4:
Try to construct triangles using match sticks. Some are shown here.

(a) 3 matchsticks?
(b) 4 matchsticks?
(c) 5 matchsticks?
(d) 6 matchsticks?
(Remember you have to use all the available matchsticks in each case). If
you cannot make a triangle, think of reasons for it.

 

Solution:
(a) 3 matchsticks – Triangle possible


(b) 4 matchsticks – Triangle not-possible


(c) 5 matchsticks – Triangle Possible


(d) 6 matchsticks – Triangle Possible

 

NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 5.7

 

NCERT 6th Maths Chapter 5 Exercise 5.7 1

Question 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.

 

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

 

Question 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 quadrilateral.
(e) Square is also a parallelogram.

 

Solution:
The reasons are as follows;
(a) All angles are right angle and opposite sides are equal.
(b) Opposite sides are equal and parallel.
(c) Four sides are equal and diagonals are perpendicular to each other.
(d) All of them have four sides.
(e) Opposite sides are equal and parallel.

 

Question 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?

 

Solution: A square is a regular quadrilateral, as it has all sides equal and all angles equal. An equilateral triangle is also one of the example of a regular quadrilateral.

 

 

 

 

 

 

NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 5.8

 

NCERT 6th Maths Chapter 5 Exercise 5.8 1

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

Solution:
The reasons are,
(a) It is not a closed figure. So, it is not a polygon.
(b) It is a polygon because it is closed by line segments.
(c) Not made by line segments. Hence, not a polygon.
(d) It is not a polygon because it not made only by line segments, it has curved surface also.

 

Question 2:
Name each polygon:

Make two more examples of each of these.

 

Solution:
The name of the polygons is,
(a) Quadrilateral
Examples,

(b) Triangle
Examples,

(c) Pentagon
Examples

(d) Octagon
Examples,

 

Question 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.

 

Solution:
Let ABCDEF be a hexagon, now, if we join any three vertices, for example D, A, B, we get a scalene triangle DAB. But, if we join the alternate vertices, we get an equilateral triangle EAC.

 

Question 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.

 

Solution:
This can be done in this way,

Here, ABCDEFGH is the octagon and after joining the vertices G with D and H with C, we will get the rectangle GHCD.

 

Question 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.

 

Solution:
Let ABCDE be the pentagon and we will join its vertices,

DB, DA, EB, EC, AC are the diagonals of the pentagon.

 

 

 

NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 5.9

 

NCERT 6th Maths Chapter 5 Exercise 5.9 1

Question 1:
Match the following:

Give two example of each shape.

 

Solution:
(a) – (ii)
(b) – (iv)
(c) – (v)
(d) – (iii)
(e) – (i)
Examples,
(a) Cone – ice-cream cone, birthday cap.
(b) Sphere – cricket ball, football
(c) Cylinder – road-roller, lawn roller.
(d) Cuboid – match-box, shoe-box
(e) Pyramid – diamonds, Egyptian pyramids.

 

Question 2:
What shape is:

(a) Your instrument box?
(b) A brick?
(c) A match box?
(d) A road-roller?
(e) A sweet laddu?

 

Solution:
(a) A cuboid.
(b) A cuboid.
(c) A cuboid.
(d) A cylinder.
(e) A sphere.

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