NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Q1 What is the disadvantage in comparing line segments by mere observation?

Answer: The disadvantage in comparing line segments by mere observation is that our estimation may be inaccurate and therefore a divider must be used.

Q2 Why is it better to use a divider than a ruler, while measuring the length of a line segment?

Answer: While measuring the length of a line segment using error might creep in due to the thickness and translucency of the ruler and because of angular viewing. We can get rid of these errors using a divider.

Q3 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.]

Answer:

Yes $AB=AC+CB$

Q4 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?

Answer: AB = 5 cm
BC = 3 cm
AC = 8 cm
Therefore AB + BC = AC
Therefore point B lies between points A and C.

Q5 Verify, whether D is the midpoint of AG.

Answer: AD = 4 - 1 = 3
DG = 7 - 4 = 3
Therefore, AD = DG
Therefore, D is the midpoint of AG.

Q6 If B is the midpoint of AC and C is the midpoint of BD, where A, B, C, D lie on a straight line, say why AB = CD?

Answer: To Prove $:AB=CD$
B is the midpoint of AC
$\therefore AB=BC$ $(i)$
C is the midpoint of BD
$\therefore BC=CD$ $(ii)$
From (i) and (ii) we can conclude $AB=CD$
Hence proved.

Q7 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.

Answer:

After measuring their sides we have found that the sum of lengths 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

Q1 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

Answer:
(a) Half.
(b) One fourth.
(c) One fourth.
(d) Three fourth.
(e) Three fourth.
(f) Three fourth.

Q2 Where will the hand of a clock stop if it
(a) starts at 12 and makes $\frac{1}{2}$ of a revolution, clockwise?
(b) starts at 2 and makes $\frac{1}{2}$ of a revolution, clockwise?
(c) starts at 5 and makes $\frac{1}{4}$ of a revolution, clockwise?
(d) starts at 5 and makes $\frac{3}{4}$ of a revolution, clockwise?

Answer:
(a) The hand of a clock will stop at 6 after starting at 12 and making $\frac{1}{2}$ of a revolution, clockwise.
(b) The hand of a clock will stop at 8 after starting at 2 and making $\frac{1}{2}$ of a revolution, clockwise.
(c) The hand of a clock will stop at 8 after starting at 5 and making $\frac{1}{4}$ of a revolution, clockwise.
(d) The hand of a clock will stop at 2 after starting at 5 and making $\frac{3}{4}$ of a revolution, clockwise.

Q3 Which direction will you face if you start facing
(a) east and make $\frac{1}{2}$ of a revolution clockwise?
(b) east and make $1\frac{1}{2}$ of a revolution clockwise?
(c) west and make $\frac{3}{4}$ 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?)

Answer:
(a) West.
(b) West.
(c) North.
(d) South.
No need to specify clockwise or anti-clockwise for the last question as after one complete revolution we would be facing in the same direction.

Q4 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?

Answer:
(a) If we are standing facing east and turn clockwise to face north we have turned through $\frac{3}{4}th$ of a revolution.
(b) If we are standing facing south and turn clockwise to face east we have turned through $\frac{3}{4}th$ of a revolution.
(c) If we are standing facing west and turn clockwise to face east we have turned through half of a revolution.

Q5 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

Answer: 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 are

(a) 1.
(b) 2.
(c) 2.
(d) 1.
(e) 3.
(f) 2.

Q6 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?

Answer: The number of right angles we can make from the given conditions are-
(a) 1.
(b) 3.
(c) 4.
(d) 2.

Q7 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?

Answer: (a) Starting from 6 and turns through 1 right angle the hour hand stops at 9.
(b) Starting from 8 and turns through 2 right angles the hour hand stops at 2.
(c) Starting from 10 and turns through 3 right angles the hour hand stops at 7.
(d) Starting from 7 and turns through 2 straight angles the hour hand stops at 7.

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

Q1 Match the following

Answer:

Q2 Classify each one of the following angles as right, straight, acute, obtuse or reflex :

Answer:

• (a) Acute.
• (b) Obtuse.
• (c) Right.
• (d) Reflex.
• (e) Straight.
• (f) Acute, acute.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise: 5.4

Q1 What is the measure of (i) a right angle? (ii) a straight angle?

Answer: (i) 90 ^o (ii) 180 ^o

Q2 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 A∠ = 53° and m B∠ = 35°, then m A∠ > m B.

Answer:

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

Q3 Write down the measures of
(a) some acute angles.
(b) some obtuse angles.
(give at least two examples of each).

Answer:

• (a) 30^o, 45^o and 60^o
• (b) 120^o, 135^o and 150^o

Q4 Measure the angles given below using the Protractor and write down the measure.

Answer:

• (a) 45 ^o
• (b) 125 ^o
• (c) 90 ^o
• (d) 60 ^o , 90 ^o and 125 ^o

Q5 Which angle has a large measure? First, estimate and then measure.

Measure of Angle A =
Measure of Angle B =

Answer:
Measure of Angle A = 40^o
Measure of Angle B = 60^o

Q6 From these two angles which has larger measure? Estimate and then confirm by measuring them.

Answer: By estimation followed by confirmation by measurement we know that the second angle is greater.

Q7 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 _______.

Answer:

• (a) An angle whose measure is less than that of a right angle is acute.
• (b) An angle whose measure is greater than that of a right angle is obtuse.
• (c) An angle whose measure is the sum of the measures of two right angles is straight.
• (d) When the sum of the measures of two angles is that of a right angle, then each one of them is acute.
• (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.

Q8 Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).

Answer:

• (a) Measure of the given along = 40 ^o
• (b) Measure of the given along = 130 ^o
• (c) Measure of the given along = 65 ^o
• (d) Measure of the given along = 135 ^o

Q9 Find the angle measure between the hands of the clock in each figure :

Answer: The angle measure between the hands of the clock in each figure is

• (a) 90 ^o
• (b) 30 ^o
• (c) 180 ^o

Q11 Measure and classify each angle:

Answer:

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

Q1 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.

Answer:

• (a) The adjacent edges of a table-top are models for perpendicular lines.
• (b) The lines of a railway track are not models for perpendicular lines as they are parallel to each other.
• (c) The line segments forming the letter ‘L’ are models for perpendicular lines.
• (d) The line segments forming the letter ‘V’ are models for perpendicular lines.

Q2 Let $\overline{PQ}$ be the perpendicular to the line segment $\overline{XY}$ . Let $\overline{PQ}$ and $\overline{XY}$ intersect in the point A. What is the measure of $\mathrm{\angle }PAY$ ?

Answer: $PQ\perp XY$
PQ and XY intersect at A
$PA\perp AY$
Therefore $\mathrm{\angle }PAY={90}^o$

Q3 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?

Answer: The angles of the two set squares are
(i) 90^o, 60^o and 30^o
(ii) 90^o, 45 ^o, and 45^o
Yes they have the common angle measure 90 ^o

Q4 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.

Answer:

• (a) CE = 5 - 3 = 2 units
  EG = 7 - 5 = 2 units
  Therefore CE = EG.
• (b) CE = EG therefore PE bisects CG.
• (c) PE is the perpendicular bisector for line segments DF and BH
• (d)
  • (i) AC = 3 - 1 = 2 units
    FG = 7 - 6 = 1 unit
    Therefore AC > FG
    True
  • (ii) CD = 4 - 3 = 1 unit
    GH = 8 - 7 = 1 unit
    Therefore CD = GH
    True
  • (iii) BC = 3 - 2 = 1 unit
    EH = 8 - 5 = 3 units
    Therefore BC < EH
    True.

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

Q1 Name the types of following triangles :

• (a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
• (b) $\mathrm{\Delta }ABC$ with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
• (c) $\mathrm{\Delta }PQR$ such that PQ = QR = PR = 5 cm.
• (d) $\mathrm{\Delta }DEF$ with $m\mathrm{\angle }D={90}^{\circ }$
• (e) $\mathrm{\Delta }XYZ$ with $m\mathrm{\angle }Y={90}^{\circ }$ and XY = YZ.
• (f) $\mathrm{\Delta }LMN$ with $m\mathrm{\angle }L={30}^{\circ }$ , $m\mathrm{\angle }M={70}^{\circ }$ and $m\mathrm{\angle }N={80}^{\circ }$

Answer:

• (a) Scalene Triangle.
• (b) Scalene Triangle.
• (c) Equilateral Triangle.
• (d) Right-angled Triangle.
• (e) Right-angled isosceles Triangle.
• (f) Acute angled Triangle.

Q2 Match the following :

Answer:

Q3 Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation)

Answer:

• (a)(i) Acute angled triangle.
• (ii) Isosceles triangle.
• (b)(i) Right-angled triangle.
• (ii) Scalane triangle.
• (c)(i) Obtuse angled triangle.
• (ii) Isosceles triangle.
• (d)(i) Right-angled triangle.
• (ii) Isosceles triangle.
• (e)(i) Acute angled triangle.
• (ii) Equilateral triangle.
• (f)(i) Obtuse angled triangle.
• (ii) Scalene triangle.

NCERT Solutions for Class 6 Maths Topic: Quadrilaterals

Q1 Place a pair of unequal sticks such that they have their endpoints joined at one end. Now place another such pair meeting the free ends of the first pair. What is the figure enclosed? It is a quadrilateral, like the one you see here. The sides of the quadrilateral are AB, BC, ___, ___. There are 4 angles for this quadrilateral. They are given by ∠BAD, ∠ADC, ∠DCB and _____. BD is one diagonal. What is the other? Measure the length of the sides and the diagonals. Measure all the angles also.

Answer: The sides of the quadrilateral are AB, BC, CD, DA
The angles are given by $\mathrm{\angle }BAD,\mathrm{\angle }ADC,\mathrm{\angle }DCBand\underset{―}{\mathrm{\angle }ABC}$
The other diagonal is AD.

Q2 Using four unequal sticks, as you did in the above activity, see if you can form a quadrilateral such that

• (a) all the four angles are acute.
• (b) one of the angles is obtuse.
• (c) one of the angles is right-angled.
• (d) two of the angles are obtuse.
• (e) two of the angles are right-angled.
• (f) the diagonals are perpendicular to one another

Answer:

(a) all the four angles are acute.

(b) one of the angles is obtuse.

(c) one of the angles is right-angled.

(d) two of the angles are obtuse.

(e) two of the angles are right-angled.

(f) the diagonals are perpendicular to one another

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

Q1 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.

Answer:

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

Q2 (a) Give reasons for the following: A square can be thought of as a special rectangle.

Answer: A square can be thought of as a special rectangle as it is a rectangle only but with all sides equal.

Q2 (b) Give reasons for the following: A rectangle can be thought of as a special parallelogram.

Answer: A rectangle can be thought of as a special parallelogram as it s a parallelogram only but with all angles equal to ninety degrees.

Q2 (c) Give reasons for the following: A square can be thought of as a special rhombus.

Answer: A square can be thought of as a special rhombus because like a rhombus it has all sides equal but all its angles are also equal.

Q2 (d) Give reasons for the following: Squares, rectangles, parallelograms are all quadrilaterals.

Answer: Squares, rectangles, parallelograms are all quadrilaterals as they all have four sides.

Q2 (e) Give reasons for the following: Square is also a parallelogram.

Answer: Square is also a parallelogram as its opposite sides are parallel.

Q3 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?

Answer: Square is the only quadrilateral with sides equal in length and angles equal in measure, therefore, a square is the regular quadrilateral.

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

Q1 Examine whether the following are polygons. If anyone among them is not, say why?

Answer:

• (a) The given figure is not a polygon as it is not a closed figure.
• (b) The given figure is a polygon.
• (c) The given figure is not a polygon as a polygon is enclosed only by line segments.
• (d) The given figure is not a polygon as a polygon is enclosed only by line segments.

Q2 Name each polygon.

Make two more examples of each of these.

Answer:

(a) Quadrilateral

(b) Triangle

(c) Pentagon

(d) Octagon

Q3 Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of triangle you have drawn.

Answer:

We have drawn the regular Hexagon ABCDEF and by joining the vertices B, D and F we have formed the Equilateral Triangle BDF.

Q4 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.

Answer:

We have made the regular octagon ABCDEFGH and by joining vertices H, C, D and G we have formed the rectangle HCDG

Q5 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.

Answer:

We have drawn the pentagon ABCDE and by joining its vertices he has drawn the diagonals AC, CE, EB, BD and DA.

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

Q1 Match the following :

(a) Cone (i)

(b) Sphere (ii)

(c) Cylinder (iii)

(d) Cuboid (iv)

(e) Pyramid (v)

Answer:

(a) Cone (ii)

(b) Sphere (iv)

(c) Cylinder (v)

(d) Cuboid (iii)

(e) Pyramid (i)

Q2 What shape is (a) Your instrument box? (b) A brick? (c) A matchbox? (d) A road-roller? (e) A sweet laddu?

Answer: The shape of the following things are

• (a) Your instrument box- Cuboid
• (b) A brick- Cuboid
• (c) A matchbox-Cuboid
• (d) A road-roller- Cylinder
• (e) A sweet laddu-Sphere