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## NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 5.1

**Question 1:**

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

**Solution**:

This will lead us to miscalculations, which we don’t want.

**Question 2:**

**Why is it better to use a divider than a ruler, while measuring the length of**

**a line segment?**

**Solution**:

The thickness of ruler may cause inconvenience, while measuring the line segment.

**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.]**

**Solution**:

As it is given in the question that C lies between the points A and B, AC + CB = AB

Measure AC, CB and AB.

AC = 6 cm

CB = 2 cm

AB = 8 cm

Thus, AC + CB = AB

**Question 4:**

**If A, B, C are three points on a line such that AB = 5 cm, BC = 3cm and AC**

**= 8 cm, which one of them lies between the other two?**

**Solution**:

As, it can be seen that AC = AB + BC, it can be said that B lies between A and C.

**Question 5:**

**Verify whether D is the mid-point of ****AG .**

**Solution**:

From the given figure we can see that, AD = 3 units and DG = 3 units, so we can say that D is the mid-point.

**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?**

Solution:

(i)

The sum of the two sides is always greater than the third side.

(ii)

The sum of the two sides is always greater than the third side.

(iii)

The sum of the two sides is always greater than the third side.

(iv)

The sum of the two sides is always greater than the third side.

(v)

The sum of the two sides is always greater than the third side.

## NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 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**

**Solution**:

The fraction of revolution that hour hand turn of a clock turn in each case is as follows,

**Question 2:**

**Where will the hand of a clock stop if it:**

**(a) Starts at 12 and make 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 1/3 of a revolution, clockwise?**

**Solution**:

(a) At 6 o’clock.

(b) At 8 o’clock.

(c) At 8 o’clock.

(d) At 2 o’clock.

**Question 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, clockwise?**

**(d) South and make one full revolution?**

**(Should we specify clockwise or anti-clockwise for this last question? Why**

**not?)**

**Solution**:

The directions are as follows,

(a) West

(b) West

(c) North

(d) South ( clockwise or anti-clockwise doesn’t matter in this case since full revolution will make bring us back to original in both cases).

**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?**

**Solution**:

The amount of revolution in each case is as followed,

(a)3/4

(b)3/4

(c)1/52

**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**

**Solution**:

The number of right angles turned in each case is,

(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?**

**Solution**:

The number of right angles turned in each case is,

(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?**

**Solution**:

The hour hand will be at,

(a) At 9 (b) At 2 (c) At 7 (d) At 7

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

**Question 1:**

**Match the following:**

**(i) Straight angle (a) less than one-fourth 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 a revolution**

**(v) Reflex angle (e) between and of a revolution**

**(f) One complete revolution**

**Solution**:

(i) – (c)

(ii) – (d)

(iii) – (a)

(iv) – (e)

(v) – (b)

**Question 2:**

**Classify each one of the following angles as right, straight, acute, obtuse or**

**reflex:**

**Solution**:

The angles are named as follows,

(a) Acute angle

(b) Obtuse angle

(c) Right angle

(d) Reflex angle

(e) Straight angle

(f) Acute angle

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

**Question 1:**

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

**Solution**:

The measure of a right angle is 900

and that of a straight angle is 1800

#### .

**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 on complete revolution = 360 .**

**(e) If m A = 53 and mB = 35 ,then m A > mB.**

**Solution**:

(a) True

(b) False

(c) True

(d) True

(e) True

**Question 3:**

**Write down the measure of:**

**(a) Some acute angles (b) Some obtuse angles**

**(Give at least two examples of each)**

**Solution**:

(a) 30 , 45

(b) 130 , 169

**Question 4:**

**Measure the angles given below, using the protractor and write down the**

**measure:**

**Solution**:

The measure of the angles is,

(a) 45 (b) 120 (c) 90 (d)1= 60 ,2= 95 , 3= 135

**Question 5:**

**Which angle has a large measure? First estimate and then measure:**

**Measure of angle A =**

**Measure of angle B =**

**Solution**:

By observation we can see that measure of angle B is greater.

A = 45

B = 60

**Question 6:**

**From these two angles which has larger measure? Estimate and then**

**confirm by measuring them:**

**Solution**:

By observation we can see that (b) has a bigger angle measure,

Measure of angle A = 450

Measure of angle B = 600

Hence, confirmed.

**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 ________.**

**Solution**:

(a) Acute angle

(b) Obtuse angle

(c) Straight angle

(d) Acute angle

(e) 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).**

**Solution**:

(i) 30 (ii) 120 (iii) 60 (iv) 150

**Question 9:**

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

**Solution**:

(a) 900

(b) 300

(c) 1800

**Question 10:**

**Investigate:**

**In the given figure, the angle measure 300. Look at the same figure through**

**a magnifying glass. Does the angle become larger? Does the size of the**

**angle change?**

**Solution**:

No, the measure of the angle will be same.

**Question 11:**

**Measure and classify each angle:**

**Solution**:

## NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 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.**

**Solution**:

The models which show perpendicular lines are,

(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.**

**Solution**:

As we can see in the question, it is given that PQ is perpendicular to XY and thus,

Thus,PAY = 900

**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?**

**Solution**:

**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

**Solution**:

(a) Yes.

(b) Yes.

(c) PE is the perpendicular bisector for CG and BH

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

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

**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)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 mD = 900**

**(e)XYZ with mY = 900 and XY = YZ**

**(f)LMN with mL = 300, m M = 700nand mN = 800**

.

**Solution**:

The type of the triangle in each case is,

(a) Scalene triangle

(b) Scalene triangle

(c) Equilateral triangle

(d) Right-angled triangle

(e) Isosceles right-angled triangle

(f) Acute-angled triangle

**Question 2:**

**Match the following:**

**Measure of Triangle Types of Triangle**

**(i) 3 sides of equal length (a) Scalene**

**(ii) 2 sides of equal length (b) Isosceles right angle**

**(iii) All sides are of different length (c) Obtuse angle**

**(iv) 3 acute angles (d) Right angle**

**(v) 1 right angle (e) Equilateral**

**(vi) 1 obtuse angle (f) Acute angle**

**(vii) 1 right angle with two sides (g) Isosceles**

**of equal length**

**Solution**:

(i) → (e)

(ii) → (g)

(iii) → (a)

(iv) → (f)

(v) → (d)

(vi) → (c)

(vii) → (b)

**Question 3:**

**Name each of the following triangles in two different ways: (You may judge**

**the nature of angle by observation).**

**Solution**:

(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

**Question 4:**

**Try to construct triangles using match sticks. Some are shown here.**

**(a) 3 matchsticks?**

**(b) 4 matchsticks?**

**(c) 5 matchsticks?**

**(d) 6 matchsticks?**

**(Remember you have to use all the available matchsticks in each case). If**

**you cannot make a triangle, think of reasons for it.**

**Solution**:

(a) 3 matchsticks – Triangle possible

(b) 4 matchsticks – Triangle not-possible

(c) 5 matchsticks – Triangle Possible

(d) 6 matchsticks – Triangle Possible

## NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes Ex 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.**

**Solution**:

(a) True

(b) True

(c) True

(d) True

(e) False

(f) False

**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 quadrilateral.**

**(e) Square is also a parallelogram.**

**Solution**:

The reasons are as follows;

(a) All angles are right angle and opposite sides are equal.

(b) Opposite sides are equal and parallel.

(c) Four sides are equal and diagonals are perpendicular to each other.

(d) All of them have four sides.

(e) Opposite sides are equal and 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?**

**Solution**: A square is a regular quadrilateral, as it has all sides equal and all angles equal. An equilateral triangle is also one of the example of a regular quadrilateral.

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

**Question 1:**

**Examine whether the following are polygons. If anyone among these is not,**

**say why? **

**Solution**:

The reasons are,

(a) It is not a closed figure. So, it is not a polygon.

(b) It is a polygon because it is closed by line segments.

(c) Not made by line segments. Hence, not a polygon.

(d) It is not a polygon because it not made only by line segments, it has curved surface also.

**Question 2:**

**Name each polygon:**

**Make two more examples of each of these.**

**Solution:**

The name of the polygons is,

(a) Quadrilateral

Examples,

(b) Triangle

Examples,

(c) Pentagon

Examples

(d) Octagon

Examples,

**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.**

**Solution**:

Let ABCDEF be a hexagon, now, if we join any three vertices, for example D, A, B, we get a scalene triangle DAB. But, if we join the alternate vertices, we get an equilateral triangle EAC.

**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.**

**Solution**:

This can be done in this way,

Here, ABCDEFGH is the octagon and after joining the vertices G with D and H with C, we will get the rectangle GHCD.

**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.**

**Solution**:

Let ABCDE be the pentagon and we will join its vertices,

DB, DA, EB, EC, AC are the diagonals of the pentagon.

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

**Question 1:**

**Match the following:**

Give two example of each shape.

**Solution**:

(a) – (ii)

(b) – (iv)

(c) – (v)

(d) – (iii)

(e) – (i)

Examples,

(a) Cone – ice-cream cone, birthday cap.

(b) Sphere – cricket ball, football

(c) Cylinder – road-roller, lawn roller.

(d) Cuboid – match-box, shoe-box

(e) Pyramid – diamonds, Egyptian pyramids.

**Question 2:**

**What shape is:**

**(a) Your instrument box?**

**(b) A brick?**

**(c) A match box?**

**(d) A road-roller?**

**(e) A sweet laddu?**

**Solution**:

(a) A cuboid.

(b) A cuboid.

(c) A cuboid.

(d) A cylinder.

(e) A sphere.