Class 6 | Mathematics | Chapter 5 | Understanding Elementary Shapes | NCERT Solutions
1. What is the disadvantage in comparing line segments by mere observation?
Answer: The disadvantage in comparing line segments by mere observation is chance of error due to improper viewing.
2. Why is it better to use a divider than a ruler, while measuring the length of a line segment?
Answer: It is better to use a divider than a ruler, because the thickness of the ruler may cause difficulties in reading of length or positioning error may occur. However divider gives up accurate measurement.
3. Draw any line segment, say A̅B̅, . 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.]
AB = 6.5 cm
AC = 3cm
CB = 3.5 cm
AC + CB = 3 cm + 3.5 cm
AB = 6.5 cm
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?
AB = 5 cm,
BC = 3 cm and AC = 8 cm
AC = AB + BC
Point B is lying between A and C
5. Verify, whether D is the mid point of A̅G̅ ?
Answer: AD = 3 units
DB= 3 units
AG= 6 units
D is the mid point of AG.
6. If B is the mid point of A̅C̅ and C is the mid point of B̅D̅ , where A,B,C,D lie on a straight line, say why AB = CD?
Answer: B is the mid point of AC
∴ AB= BC ————(1)
And C is the mid-point of BD
BC= CD ————–(2)
From the equation we get,
AB = CD
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.
Answer : Yes, sum of two sides of a triangle is always greater than the third side.
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
a) When the hour hand goes from 3 to 9 , it will rotate by 2 right angles.
b) When the hour hand goes from 4 to 7 , it will rotate by 1 right angles.
c) When the hour hand goes from 7 to 10 , it will rotate by 1 right angles.
d) When the hour hand goes from 12 to 9 , it will rotate by 3 right angles.
e) When the hour hand goes from 1 to 10 , it will rotate by 3 right angles.
f) When the hour hand goes from 6 to 3 , it will rotate by 3 right angles.
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?
(a) At 6
(b) At 8
(c) At 8
(d) At 2
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 and 1/2 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?)
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?
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
Answer 5: a) One right angle
(b) Two right angles
(c) Two right angles
(d) One right angle
(e) Three right angles
(f) Two right angles
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?
(a) One right angle
(b) Three right angles
(c) Four right angles
(d) Two right angles
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?
(a) At 9
(b) At 2
(c) At 7
(d) At 7
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
Answers 1: (i) : (c)
(ii) : (d)
(iii) : (a)
(iv) : (e)
(v) : (b)
2. Classify each one of the following angles as right, straight, acute, obtuse or reflex:
Answer 2 : (a) Acute angle
(b) Obtuse angle
(c) Right angle
(d) Reflex angle
(e) Straight angle
(f) Acute angle
1. What is the measure of (a) a right angle? (b) a straight angle?
Answer 1) (a) 90°
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 ∠A = 53° and m ∠B = 35°, then m ∠A > m ∠B.
Answer 2 (a) True (b) False (c) True (d) True (e) True
3. Write down the measures of
(a) some acute angles.
(b) some obtuse angles.
(give at least two examples of each).
Answer 3) a) 50° , 75°
b) 120°, 145°
4. Measure the angles given below using the Protractor and write down the measure.
Answer 4: (a) 40°
5. Which angle has a large measure?
First estimate and then measure.
Measure of Angle A =
Measure of Angle B =
Answer 5 : ∠B has larger measure.
∠A = 40° and ∠B = 65°
6. From these two angles which has larger measure? Estimate and then confirm by measuring them.
Answer 6) Second angle has larger measure.
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
(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 7) (a) acute angle
(b) obtuse angle
(c) straight angle
(d) acute angle
(e) 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).
Answer 8 : (i) 30°
9. Find the angle measure between the hands of the clock in each figure :
Answer 9) (i) 90° (Right angle)
(ii) 30° (Acute angle)
(iii) 180° (Straight angle)
10. Investigate In the given figure, the angle measures 30°. Look at the same figure through a magnifying glass. Does the angle becomes larger? Does the size of the angle change?
Answer 10 ) No, the measure of angle will be same.
11. Measure and classify each angle :
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.
1) (a) Perpendicular
(b) Not perpendicular
(d) Not perpendicular
2. Let P̅Q̅ be the perpendicular to the line segment X̅Y̅ . Let P̅Q̅and X̅Y̅ intersect in the point A. What is the measure of ∠PAY ?
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?
3) One set-square has 45° ,90° ,45° and other set-square has 60° ,90° ,30° . They have 90° as common angle.
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.
4) (a) Yes, both measure 2 units.
(b) Yes, because CE = EG
(c) DF and CG , BH
(d) (i) True, (ii) True, (iii) True
1. Name the types of following triangles :
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) ΔABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) ΔPQR such that PQ = QR = PR = 5 cm.
(d) ΔDEF with m ∠D = 90°
(e) ΔXYZ with m ∠Y = 90° and XY = YZ
(f) ΔLMN with m ∠L = 30°, m ∠M = 70° and m∠N = 80°.
Answer 1) (a) Scalene triangle
(b) Scalene triangle
(c) Equilateral triangle
(d) Right-angled triangle
(e) Isosceles right-angled triangle
(f) Acute-angled triangle
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
Answer 2) (i) : (e)
(ii) : (g)
(iii) : (a)
(iv) : (f)
(v) : (d)
(vi) : (c)
(vii) : (b)
3. Name each of the following triangles in two different ways: (you may judge the
nature of the angle by observation)
Answer 3) (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
4. Try to construct triangles using sticks. Some are shown here. 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.
Answer) (a) 3 matchsticks This is an acute angle triangle and it is possible with 3 matchsticks to make a triangle because sum of two sides is greater than third side.
(b) 4 matchsticks This is a square, hence with four matchsticks we cannot make triangle.
(c) 5 matchsticks This is an acute angle triangle and it is possible to make triangle with five matchsticks, in this case sum of two sides is greater than third side.
(d) 6 matchsticks This is an acute angle triangle and it is possible to make a triangle with the help of 6 matchsticks because sum of two sides is greater than third side.
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.
Answer (a) True
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.
Answer : (a) Because its all angles are right angle and opposite sides are equal.
(b) Because its opposite sides are equal and parallel.
(c) Because its four sides are equal and diagonals are perpendicular to each other.
(d) Because all of them have four sides.
(e) Because its opposite sides are equal and parallel
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?
Answer: A square is a regular quadrilateral.
1. Examine whether the following are polygons. If any one among them is not, say
Answer) (a) As it is not a closed figure, therefore, it is not a polygon.
(b) It is a polygon because it is closed by line segments.
(c) It is not a polygon because it is not made by line segments.
(d) It is not a polygon because it not made only by line segments, it has curved surface also
2. Name each polygon. two more examples of each of these.
Answer: (a) Quadrilateral
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.
Answer: ABCDEF is a regular hexagon and triangle thus formed by joining AEF is an isosceles triangle.
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.
Answer: ABCDEFGH is a regular octagon and CDGH is a rectangle.
5. A diagonal is a line segment that joins any two vertices of the polygon and is not a side the polygon. Draw a rough sketch of a pentagon and draw its diagonals.
Answer) ABCDE is the required pentagon and its diagonals are AD, AC, BE and BD.
1. Match the following :
Give two new examples of each shape.
2. What shape is
(a) Your instrument box?
(b) A brick?
(c) A match box?
(d) A road-roller?
(e) A sweet laddu?
Answer : (a) Cuboid