NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

It is better to use a divider than a ruler, because the thickness of the ruler may cause difficulties in reading off her length. However divider gives up accurate measurement.

Q.3 Draw any line segment, say \(\overline {AB} \). 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 AC + CB = AB, then we can be sure that C lies between A and B]

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

There , A, B and C such that C lies between A and B and AB = 9 cm.

AC = 5 cm, CB = 4 cm.

\(\therefore \) AC + CB = 5 cm + 4 cm = 9 cm.

And AB = 9 cm.

Hence, AB = AC + CB Proved.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

we have AG = 7 unit – 1 unit = 6 unit

AD = 4 unit – 1 unit = 3 unit

and DG = 7 unit – 4 unit = 3 unit

\(\therefore \)AG = AD + DG.

Hence, D is the mid point of AG.

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

Guven B is the mid point of AC .

\(\therefore \) AB = BC …(i)

Given, C is the mid-point of BD .

BC = CD .... (ii)

From Eq.(i) and (ii), We have

AB = CD

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(I) In first figure,

It is an equalatral triangle

Sum of two side = 5 + 5 = 10

10 > 5
Hence, the sum of any two sides of a triangle is greater than the third side.

(II) In second figure ,

Sum of two side = 5 + 5 = 10 , 5 + 3 = 8 , 5 + 3 = 8

\(\therefore \) 10 > 3, 8 > 5 , 8 > 5

Hence, the sum of any two sides of a triangle is greater than the third side.

(III) In third figure,

Sum of two side = 6 + 10 = 16 , 8 + 10 = 18 , 6 + 8 = 14

\(\therefore \) 16 > 8, 18 > 6, 14 > 10

Hence, the sum of any two sides of a triangle is greater than the third side.

(IV) In forth figure,

Sum of two side = 6 + 7 = 13 , 7 + 6 = 13 , 6 + 6 = 12

\(\therefore \) 13 > 6, 13 > 6, 12 > 7

Hence, the sum of any two sides of a triangle is greater than the third side.

(IV) In fifth figure,

Sum of two side = 12 + 5 = 17 , 13 + 5 = 18 , 12 + 13 = 25

\(\therefore \) 17 > 13, 18 > 12, 25 > 5

Hence, the sum of any two sides of a triangle is greater than the third side.

Therefore we conclude that the sum of any two sides of a triangle is always greater than the third side.

Q.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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) 3 to 9

9 – 3 = 6 hour

In one revolution = 12 hour

No. of revolution = 6 / 12 = 1/2 revolution.

(b) 4 to 7

7 – 4 = 3 hour

In one revolution = 12 hour

No. of revolution = 3 / 12 = 1/4 revolution.

(c) 7 to 10

10 – 7 = 3 hour

In one revolution = 12 hour

No. of revolution = 3 / 12 = 1/4 revolution.

(d) 12 to 9 i.e., 0 to 9

9 – 0 = 9 hour

In one revolution = 12 hour

No. of revolution = 9 / 12 = 3/4 revolution.

(e) 1 to 10

10 – 1 = 9 hour

In one revolution = 12 hour

No. of revolution = 9 / 12 = 3/4 revolution.

(f) 6 to 3 i.e., 6 to 12 and then 12 to 3

6 to 12 = 12 – 6 = 6 hour and 12 to 3 = 0 to 3 = 3 – 0 = 3 hour

6 + 3 = 9 hour

In one revolution = 12 hour

No. of revolution = 9 / 12 = 3/4 revolution.

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) Starting from 12 and making 1/2 of a revolution,

In one revolution = 12 hour

\(\therefore \) 1/2 revolution =( 1/2 ) × 12 = 6 hour

Then 12 + 6 I.e., 0 + 6 = 6

the clock hand stops at 6.

(b) Starting from 2 and making 1/2 of a revolution,

In one revolution = 12 hour

\(\therefore \) 1/2 revolution =( 1/2 ) × 12 = 6 hour

Then 2 + 6 = 8

the clock hand stops at 8.

(c) Starting from 5 and making 1/4 of a revolution,

In one revolution = 12 hour

\(\therefore \) 1/4 revolution =( 1/4 ) × 12 = 3 hour

Then 5 + 3 = 8

the clock hand stops at 8.

(d) Starting from 12 and making 3/4 of a revolution,

In one revolution = 12 hour

\(\therefore \) 3/4 revolution =( 3/4 ) × 12 = 9 hour

Then 5 + 9 = 14 = 12 + 2 I.e., 0 +2 = 2

the clock hand stops at 2.

Q.3 Which direction will you face if you start facing

(a) east and make \(\frac{1}{2} \) of a revolution clockwise? z

(b ) east and make\(1\frac{1}{2} \) of a revolution clockwise? z

(c) west and make \(\frac{3}{4} \) of a revolution anticlockwise?

(d) south and make one full revolution? (Should we specify clockwise or anticlockwise for this last question? Why not?)

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) west

(b) west

(c) north

(d) south

In case of revolving 1 complete revolution, either clockwise or anti-clockwise we will be back at the original position.

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) If we start from East and turn clockwise to face North, 3 /4 of a revolution is required.

(b) If we start from south and turn clockwise to face east, 3/4 of a revolution is required.

(c) If we start from west and turn clockwise to face east, 1/2 of a revolution is required.

Q.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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) 3 to 6 = 6 - 3 = 3 hour

In one revolution = 12 hour

No. of revolution = 3 / 12 = 1/4 revolution.

In one revolution = 4 right angle

\(\therefore \) 1/4 revolution = (1\4) × 4 = 1 right angle

(b) 2 to 8 = 8 - 2 = 6 hour

In one revolution = 12 hour

No. of revolution = 6 / 12 = 1/2 revolution.

In one revolution = 4 right angle

\(\therefore \) 1/2 revolution = (1\2) × 4 = 2 right angle

(c) 5 to 11 = 11 - 5 = 6 hour

In one revolution = 12 hour

No. of revolution = 6 / 12 = 1/2 revolution.

In one revolution = 4 right angle

\(\therefore \) 1/2 revolution = (1\2) × 4 = 2 right angle

(d) 10 to 1 I.e., 10 to 13 = 13 - 10 = 3 hour

In one revolution = 12 hour

No. of revolution = 3 / 12 = 1/4 revolution.

In one revolution = 4 right angle

\(\therefore \) 1/4 revolution = (1\4) × 4 = 1 right angle

(e) 12 to 9 I.e., 0 to 9 = 9 - 0 = 9 hour

In one revolution = 12 hour

No. of revolution = 9 / 12 = 3/4 revolution.

In one revolution = 4 right angle

\(\therefore \) 3/4 revolution = (3\4) × 4 = 3 right angle

(f) 12 to 6 = 6 - 0 = 6 hour

In one revolution = 12 hour

No. of revolution = 6 / 12 = 1/2 revolution.

In one revolution = 4 right angle

\(\therefore \) 1/2 revolution = (1\2) × 4 = 2 right angle

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) we know that in clock wise direction North to East one right angle , East to South

Q.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 \(\frac{1}{4} \) and \(\frac{1}{4} \) of a revolution

(f) One complete revolution

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(i) Straight angle \(\rightarrow \) (c) Half of a revolution.

(ii) Right angle \(\rightarrow \) (d) One-fourth of revolution.

(iii) Acute angle \(\rightarrow \) (a) Less than one-fourth of a revolution.

(iv) Obtuse angle \(\rightarrow \) (e) Between 14 and 12 of a revolution.

(v) Reflex angle \(\rightarrow \) (f) One complete revolution, right, acute, obtuse or reflex.

Q.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 \(\angle \) A = 53° and m \(\angle \) B = 35°, then m \(\angle \) A > m \(\angle \)B.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) True

(b) False

(c) True

(d) True

(e) True

Q.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 ______

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) An angle whose measure is less than that of a right angle is acute angle

(b) An angle whose measure is greater than that of a right angle is obtuse angle (but less than 180°)

(c) An angle whose measure is the sum of the measures of two right angles is straight angle

(d) When the sum of the measures of two angles is that of a right angle, then each one of them is acute angle

(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 angle.

Q.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).

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

The measures of the angles shown in above figure are 40°, 130°, 65° and 135°

Q.10 In the given figure, the angle measure 30°. Look at the same figure through a magnifying glass. Does the angle becomes larger? Does the size of the angle change?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

The measure of an angle will not change by viewing through a magnifying glass

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) and (c) are models for perpendicular lines.

Q.2 Let \(\overline {PQ} \)be the perpendicular to the line segment\(\overline {XY} \). Let\(\overline {PQ} \)and \(\overline {XY} \) intersect at in the point A. What is the measure of \(\angle \)PAY?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

\(\angle \)PAY = 90°

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

The measure angles of triangle (a) are : 30°, 60° and 90°.

The measure angles of triangle (b) are 45°, 45° and 90°.

Yes, they have a common angle of measure 90°.

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) Yes

(b) Yes,

(c)\(\overline{BG} \) and \(\overline {DF} \)

(d) (i) True (ii) True (iii) True

Q.1 Name the types of following triangles:

(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.

(b) \(\triangle \) ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.

(c) \(\triangle \)PQR such that PQ = QR = PR = 5 cm.

(d) \(\triangle \)DEF with \(\angle \)D = 90°

(e) \(\triangle \)XYZ with \(\angle \)Y = 90° and XY = YZ.

(f) \(\triangle \)LMN with \(\angle \)L = 30°, ?M = 70° and ?N = 80°.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) Scalene triangle

(b) Scalene triangle

(c) Equilateral triangle

(d) Right angled triangle

(e) Right angled isosceles triangle

(f) Acute angled triangle

Q.2 Match the following:

Measures of Triangle Type of Triangle

(i) 3 sides of equal length \(\rightarrow \) (a) Scalene
(ii) 2 sides of equal length \(\rightarrow \) (b) Isosceles right angled
(iii) All sides are of different \(\rightarrow \) (c) Obtuse angled
(iv) 3 acute angles \(\rightarrow \) (d) Right angled
(v) 1 right angle \(\rightarrow \) (e) Equilateral
(vi) 1 obtuse angle \(\rightarrow \) (f) Acute angled
(vii) 1 right angle with two sides of equal length \(\rightarrow \) (g) Isosceles

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(i) \(\rightarrow \) Equilateral triangle

(ii) \(\rightarrow \) Isosceles triangle

(iii) \(\rightarrow \) Scalene triangle

(iv) \(\rightarrow \) Acute angled triangle

(v) \(\rightarrow \) Right angled triangle

(vi) \(\rightarrow \) Obtuse angled triangle

(vii) \(\rightarrow \) Isosceles right angled triangle

Q.3 Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation)

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(i) Acute angled and isosceles triangle

(ii) Right angled and scalene triangle

(iii) Obtuse angled and isosceles triangle

(iv) Right angled and isosceles triangle

(v) Equilateral and acute angled triangle

(vi) Obtuse angled and scalene triangle

Q.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 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

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) Yes, we can make an equilateral triangle with 3 matchsticks.

(b) No, we cannot make a triangle with 4 matchsticks.

(c) Yes, we can make an isosceles triangle with five matchsticks.

(d) Yes, we can make an equilateral triangle with 6 matchsticks.

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) True

(b) True

(c) True

(d) True

(e) False

(f) False

Q.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.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) A square has all the properties as that of rectangle. So, it is a special rectangle.

(b) A rectangle has the same properties as that of parallelogram. So, it is a special parallelogram.

(c) A square has the same properties as that of a rhombus. So, it is a special rhombus.

(d) Square, rectangles and parallelogram are all quadrilateral as they are all enclosed by four sides.

Q.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?

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

Square is only the regular quadrilateral with equal sides and equal angles. Therefore, square is a regular quadrilateral.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

Answer :

(a) The given figure is not closed. Therefore, it is not a polygon.

(b) The given figure is a polygon.

(c) The given figure is not a polygon because every polygon is enclosed with line segments.

(d) The given figure is not a polygon because it is enclosed by an arc and two line segments.

There are total 44 questions present in ncert solutions for class 6 maths chapter 5 understanding elementary shapes

There are total 4 long question/answers in ncert solutions for class 6 maths chapter 5 understanding elementary shapes

There are total 9 exercise present in ncert solutions for class 6 maths chapter 5 understanding elementary shapes