NCERT Solutions for Understanding Elementary Shapes Chapter 5

Table of Content

• Exercise 5.1
• Exercise 5.2
• Exercise 5.3
• Exercise 5.4
• Exercise 5.5
• Exercise 5.6
• Exercise 5.7
• Exercise 5.8
• Exercise 5.9

Exercise 5.1

Question 1
What is the disadvantage in comparing line segments by mere observation?
Answer
You may be correct when the difference is obvious
But comparison become difficult when the difference in lengths between these two may not be obvious.
 
Question 2
Why is it better to use a divider than a ruler, while measuring the length of a line segment?
Answer
Ruler can be error prone because of two reasons
(a) thickness of the ruler
(b) Incorrect positioning of the eye will give wrong measurement
So, it is better to use divider than a ruler
 
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.]
Answer
Draw the line and then measure each line segment to check it
 
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?
Answer
Given that,
AB =5 cm
BC = 3 cm
AC = 8 cm
Here, AC = AB + BC
Therefore, point B is lying between A and C.
 
 
Question 5.
Verify, whether D is the midpoint of AG.

Answer
We have
AD= 3 units
DG= 3 units
AG =6 units
So, D is the midpoint of AG
 
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?
Answer

AB =BC (as B is mid-point)
BC=CD (as C is the mid-point)
Therefore
AB=CD
 
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.
 

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
 
Answer
(a) 1/2 or two right angles.
(b) 1/4 or one right angle.
(c) 1/4 or one right angle.
(d) 3/4 or three right angles.
(e) 3/4 or three right angles.
(f) 3/4 or three right angles.
 
Question 2. Where will the hand of a clock stop if it?
(a) starts at 12 and makes ½ of a revolution, clockwise?
(b) starts at 2 and makes ½ of a revolution, clockwise?
(c) starts at 5 and makes ¼ of a revolution, clockwise?
(d) starts at 5 and makes ¾ of a revolution, clockwise?
Answer
(a) At 6
(b) At 8
(c) At 8
(d) At 2
 
Question 3
Which direction will you face if you start facing
(a) east and make ½ of a revolution clockwise?
(b) east and make $1 \frac {1}{2}$ of a revolution clockwise?
(c) west and make ¾ 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
 
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?
Answer
a) ¾
b) ¾
c) ½
 
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
Answer
(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?
Answer
(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?
Answer
(a) At 9
(b) At 2
(c) At 7
(d) At 7
 

Exercise 5.3

Question 1
Match the correct options

(A) Straight angle	(i) Less than one-fourth of a revolution
(B) Right angle	(ii) More than half a revolution
(C) Acute angle	(iii) Half of a revolution
(D) Obtuse angle	(iv) One-fourth of a revolution
(E) Reflex angle	(v) Between 14 and 12 of a revolution
	(vi) One complete revolution

 
Answer
(A) Straight angle — iii) Half of a revolution
As $180^0$ is considered as a straight line and half of revolution is also $180^0$
(B) Right angle — iv) One-fourth of a revolution
As Right angle and One-fourth of a revolution are both $90^0$
(C) Acute angle — i) Less than one-fourth of a revolution
As The angle which is less than 90 is called acute angle and less than one-fourth of a revolution is the angle less than $90^0$
(D) Obtuse angle — v) Between 14 and 12 of a revolution
Obtuse angle   is the angle which is greater than 90 and less than 180 and the value between 14 and 12 of a revolution also lies between 90 and 180
(E) Reflex angle – ii) More than half a revolution
Reflex angle is the angle which is greater than $180^0$ but less than $360^0$ and more than half a revolution is the angle whose measure is greater than $180^0$
 
Question 2
Classify each one of the following angles as right, straight, acute, obtuse or reflex:

Answer
(a) Acute
(b) obtuse
(c) Right angle
(d) reflex angle
(e) straight angle
(f) Acute
 

Exercise 5.4

 
Question 1.
What is the measure of
(i) a right angle?
(ii) a straight angle?
Answer
(a) $90^0$
(b) $180^0$
 
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 one complete revolution = 360°.
(e) If m∠ÐA = 53° and m∠ÐB = 35°, then m∠ÐA > Ðm∠B.
Answer
(a) true
(b) false
(c) true
(d) true
(e) True
 
Question 3.
Write down the measures of
(a) some acute angles.
(b) some obtuse angles.
(give at least two examples of each).
Answer
(i) Acute angles
$60^0$
$45^0$
(ii) Obtuse angles
$120^0$
$160^0$
Question 4.
Measure the angles given below using the Protractor and write down the measure

Answer
a) $40^0$
b) $130^0$
c) $90^0$
d) $60^0$
 
Question 5
Which angle has a large measure?

First estimate and then measure.
Measure of Angle A =
Measure of Angle B =
Answer
A measure $40^0$
B measures $60^0$
∠A has the largest angle.
 
Question 6
From these two angles which has larger measure? Estimate and then confirm by measuring them.

Answer
The angles are $70^0$ and $75^0$
 
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 _______.
Answer
(a) acute
(b) obtuse (if the angle is less than 180°)
(c) straight
(d) acute
(e) an 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).

Answer
The angle measures
(i)$30^0$
(ii)$120^0$
(iii)$60^0$
(iv)$180^0$
 
Question 9
Find the angle measure between the hands of the clock in each figure:

Answer
90°, 30°, 180°
 
Question 10
Investigate
In the given figure, the angle measures 30°. Look at the same figure through a magnifying glass.
Does the angle become larger? Does the size of the angle change?

Answer
The angle does not change
 
Question 11
Measure and classify each angle

Angle	Measure	Type
∠AOB	–	–
∠AOC	–	–
∠BOC	–	–
∠DOC	–	–
∠DOA	–	–
∠DOB	–	–

 
Answer

Angle	Measure	Type
∠AOB	50	Acute
∠AOC	130	Obtuse
∠BOC	80	Acute
∠DOC	100	Obtuse
∠DOA	145	Obtuse
∠DOB	180	Straight

 
 

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.
Answer
(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?
Answer
90
 
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?
Answer
One is a 30° – 60° – 90° set square; the other is a 45° – 45° – 90° set square.
The angle of measure 90° (i.e. a right angle) is common between them.
 
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.
Answer
(a) Yes, as same units
(b) Yes, as CE =EG
(c) BH, DF
(d) All are true.
(i)True, (ii) True, (iii) True
 
 

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) $\Delta ABC$ with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) $\Delta PQR$ such that PQ = QR = PR = 5 cm.
(d) $\Delta DEF$ with m∠d= 90°
(e) $\Delta XYZ$ with m∠Y= 90° and XY = YZ.
(f) $\Delta LMN$ with m∠L = 30°, m∠M = 70° and m∠N= 80°.
Answer
(a) Scalene triangle
(b) Scalene triangle
(c) Equilateral triangle
(d) Right triangle
(e) Isosceles right 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
Answer:
(i)3 sides of equal length                (e) Equilateral
(ii) 2 sides of equal length               (g) Isosceles
(iii) All sides are of different length   (a) Scalene
(iv) 3 acute angles                           (f) Acute angled
 (v) 1 right angle                               (d) Right angled
 (vi) 1 obtuse angle                           (c) Obtuse angled
(vii) 1 right angle with two sides of equal length   (b) Isosceles right angled
 
Question 3
Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation)

Answer
(a) Acute-angled and isosceles.
(b) Right-angled and scalene.
(c) Obtuse-angled and isosceles.
(d) Right-angled and isosceles.
(e) Equilateral and acute angled.
(f) Obtuse-angled and scalene.
 
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 must 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) Possible (equilateral triangle)
(b) not possible. We cannot build the triangle, as then sum of two sides would be equal to another side). Square is possible
(c) possible. Isosceles triangle (2-2-1 sticks)
(d) possible. Equilateral triangle (2-2-3 sticks)

 

Exercise 5.7

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.
Answer
(a) True
(b) True
(c) True
(d) True
(e) False as opposite sides are equal only
(f) False. Both the opposite sides are not parallel
 
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 quadrilaterals.
(e) Square is also a parallelogram.
Answer
(i) A square has all the properties of a rectangle as its opposite sides are equal also all the angles are right angled.
(ii) A rectangle has also its opposite sides equal as well as parallel. So, it has all the properties of the parallelogram,
(iii) In a rhombus all the sides are equal also diagonals are perpendicular to each other. And square have the same property.
(iv) All these are four-sided polygons made of line segments.
(v) A square also has its opposite sides equal as well as 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?
Answer
A square is a regular quadrilateral.
 

Exercise 5.8

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

Answer
(a) As the figure is not closed, therefore, the shape is not a polygon.
(b) As it is closed by line segments hence it is a polygon.
(c) As it is not made of line of segments it is not a polygon.
(d)As it has curved surface and is made up of line of segments.it is not a polygon
 
Question 2
Name each polygon.

 Answer
(a) Quadrilateral
(b) Triangle
(c) Pentagon
(d) Octagon
 
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.
 
Answer

The triangle drawn is right angle triangle
 
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.
Answer

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.
Answer

 

Exercise 5.9

 
Question 1
Match the column

Answer

Question 2
What shape is
(a) Your instrument boxes?
(b) A brick?
(c) A match boxes?
(d) A road-roller?
(e) A sweet laddu?
 
Answer
(a) Cuboid
(b) Cuboid
(c) Cuboid
(d) Cylinder
(e) Sphere
 

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