Ncert Class 6 Mathematics Solutions Chapter 5 Understanding Elementary Shapes
Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of NCERT Class 6 Mathematics Book, Chapter 5, Understanding Elementary Shapes. Here students can easily find step by step solutions of all the problems for Understanding Elementary Shapes, Exercise 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7 and 5.8 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 5 solutions. Here all the solutions are based on NCERT latest syllabus.
Understanding Elementary Shapes Exercise 5.1 Solution :
(1) What is the disadvantage in comparing line segments by mere observation?
Solution :
There is a chances of errors in comparing line segments by mere observation.
(2) Why is it better to use a divider than a ruler, while measuring the length of a line segment?
Solution :
Measuring the length of a line segment it is better to use divider than a ruler because correct measurement will be possible.
(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?
Solution :
Yes. AB = AC + CB
Because C is ‘between’ A and B .i.e. C is the midpoint of line AB.
(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?
Solution :
A, B, C are the points lies on the line.
AB = 5 CM
BC = 3 CM
AC = 8 CM
AC = AB + BC
Point B is between A and C.
(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 :
B is midpoint of line AC.
AB = BC
C is midpoint of line BD.
BC = CD
Therefore, AB = CD
Understanding Elementary Shapes Exercise 5.2 Solution :
(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 :
(a) 3 to 9
One revolution is 360.
3 to 9 is 180 i.e. Half Revolution.
3 to 9 = 1 /2
(b) 4 to 7
One revolution is 360.
4 to 7 is 90 i.e. one fourth Revolution.
4 to 7 = 1 /4
(c) 7 to 10
One revolution is 360.
7 to 10 is 90 i.e. one fourth Revolution.
7 to 10 = 1 /4
(d) 12 to 9
One revolution is 360.
12 to 9 is 270 i.e. Three- fourth Revolution.
12 to 9 = 3 /4
(e) 1 to 10
One revolution is 360.
1 to 10 = 3 /4
(f) 6 to 3
One revolution is 360.
6 to 3 is 270 i.e. Three- fourth Revolution.
6 to 3 = 3 /4
(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?
Solution :
(a) Starts at 12 hand of a clock stop when 1/ 2 of a revolution at 6.
(b) Starts at 2 hand of a clock stop when 1/ 2 of a revolution at 8
(c) Starts at 5 hand of a clock stop when 1/ 4 of a revolution at 8
(d) Starts at 5 hand of a clock stop when 3/ 4 of a revolution 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 1 /2 of a revolution clockwise?
(c) West and make 3 /4 of a revolution anti-clockwise?
(d) South and make one full revolution?
Solution :
(a) if we start facing east and make 1 /2 of a revolution clockwise we are in west.
(b) if we start facing east and make 1 1 /2 of a revolution clockwise we are in west.
(c) if we start facing west and make 3 /4 of a revolution clockwise we are in North.
(d) if we start facing south and make one full revolution we are in South.
(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 :
(a) East and turn clockwise to face north we turned through 3/4.
(b) South and turn clockwise to face east we turned through 3/4.
(c) West and turn clockwise to face east we turned through 1/2.
(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 :
(a) The number of right angles turned through 3 to 6 is 1
(b) The number of right angles turned through is 2
(c) The number of right angles turned through is 2
(d) The number of right angles turned through is 1
(e) The number of right angles turned through is 3
(f) The number of right angles turned through is 2
(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 :
(a) Start facing south and turn clockwise to west right angles made are 1.
(b) Start facing north and turn anti-clockwise to east right angles made are 3.
(c) Start facing west and turn to west right angles made are 4.
(d) Start facing south and turn to north right angles made are 2.
(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 :
(a) If hour hand of a clock starts from 6 and turns through 1 right angle, then it will stop at 9.
(b) If hour hand of a clock starts from 8 and turns through 2 right angles, then it will stop at 2.
(c) If hour hand of a clock starts from 10 and turns through 3 right angles, then it will stop at 7.
(d) If hour hand of a clock starts from 7 and turns through 2 straight angles, then it will stop at 7.
Understanding Elementary Shapes Exercise 5.3 Solution :
(1) What is the measure of (i) a right angle? (ii) a straight angle?
Solution :
(i) The measure of a right angle is 90 degrees.
(ii) The measure of a straight angle is 180 degrees.
(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∠ .
Solution :
(a) Statement is – True
(b) Statement is – True
(c) Statement is – True
(d) Statement is – True
(e) Statement is – True
(3) Write down the measures of
(a) some acute angles.
(b) some obtuse angles.
Solution :
(a) Acute angles are the angles less than 90°.
Example = 40°, 50°, 60°.
(b) Obtuse angles are the angles more than 90 degree
Example : 100°, 110°, 150°.
(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
(11) Measure and classify each angle :
| Angle : | Measure : | Type : |
| ∠AOB | ||
| ∠AOC | ||
| ∠BOC | ||
| ∠DOC | ||
| ∠DOA | ||
| ∠DOB |
Solution :
Angle ∠AOB :
Measure = 40°
Type = Acute
Angle ∠AOC :
Measure = 120°
Type = Obtuse
Angle ∠BOC :
Measure = 90°
Type = Right
Angle ∠DOC :
Measure = 90°
Type = Right
Angle ∠DOA :
Measure = 110°
Type = Obtuse
Angle ∠DOB :
Measure = 180°
Type = Straight
Understanding Elementary Shapes Exercise 5.5 Solution :
(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 :
(a) The adjacent edges of a table top.
= The adjacent edges of a table top is model of perpendicular line.
(b) The lines of a railway track.
= Not a model of perpendicular line.
(c) The line segments forming the letter ‘L’.
= The line segments forming the letter ‘L’ is model of perpendicular line.
(d) The letter V.
= Not a model of perpendicular line.
(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 :
PQ be the perpendicular to the line segment XY.
PQ and XY intersect in the point A.
When line is perpendicular to the line segment it makes 90° angle.
Measure of ∠PAY = 90°
(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 :
As per the given question,
There are two set-squares.
One is 30° – 60° – 90° set square
Other is 45° – 45° – 90° set square.
Angle 90° is common i.e. Right angle is common between them.
Understanding Elementary Shapes Exercise 5.6 Solution :
(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∠ = 90°
(e) ∆XYZ with m ∠Y = 90° and XY = YZ.
(f) ∆LMN with m ∠L = 30°, m ∠M = 70° and m ∠N = 80°.
Solution :
(a) All sides are different in length.
Triangle is called as Scalene Triangle.
(b) Scalene Triangle.
(c) All sides are equal in length.
Triangle is called as Equilateral Triangle.
(d) Angle is Right angle
Triangle is called as Right angled Triangle
(e) Angle is Right angle and two sides are equal.
Triangle is called as Isosceles Right angled Triangle.
(f) All angles are acute angles.
Triangle is called as 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) ll sides are of different | (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 |
Solution :
| Measures of Triangle | Type of triangle |
| (i) 3 sides of equal length | (e) Equilateral |
| (ii) 2 sides of equal length | (g) Isosceles |
| (iii) ll sides are of different | (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 |
Understanding Elementary Shapes Exercise 5.7 Solution :
(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) Given statement is – True
(b) Given statement is – True
(c) Given statement is – True
(d) Given statement is – True
(e) Given statement is – False
(f) Given statement is – False
(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.
Solution :
(a) Reason : A square has all the properties of a rectangle.
(b) Reason : A rectangle has all the properties of a parallelograms
(c) Reason : A square has all the properties of a rhombus
(d) Reason : All the few is did closed plane figures are called quadrilaterals.
(e) Reason : A square has all the properties of a parallelogram.
(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 all of whose sides are equal in length and all off whose angles are equal in measure.
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