Ncort Solutions Class 6 Mathematics Chapter 5 Basic Comprensión for Free PDF Decarding (2023)

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Ncort Solution Class 6 Mathematics Chapter 5 - Understanding Elementary Forms

Exercise 5.1 Solutions

Exercise 5.2 Solutions

Exercise 5.3 Solutions

Exercise 5.4 Solutions

Exercise 5.5 Solutions

Exercise 5.6 Solutions

Exercise 5.7 Solutions

Exercise 5.8 Solutions

Exercise 5.9 Solutions

Access to NCERT solutions for Class 6 Chapter 5: Understanding of Elementary Forms

Exercise 5.1 Page No. 88

1. What is the disadvantage to compare line segments with mere observation?

Solutions:

With mere observation, we cannot compare line segments with a low length difference. We cannot tell which line segment has a longer length.

2. Why is it better to use a divider than a rule and at the same time measure the duration of a line segment?

Solutions:

Due to the thickness of the rule and view of the angle, there are error options when using a rule.

3. Draw all line segments, for example.

Solutions:

As point C is between A and B., all points are in the segment of the same line
Therefore, we can say to any situation where C is between A and B

AB = AC + CB

For example:

AB is a segment of 7 cm and c in length is a point between A and B, so that ca = 3 cm and cb = 4 cm.

Daher AC + CB = 7 cm

Supplied, from = 7 cm

∴ AB = AC + CB Em and check.

4. If A, B, C are three points on a line, so that = 5 cm, BC = 3 cm and ca = 8 cm, which is between the other two?

Solutions:

Data from = 5 cm

BC = 3 cm

CA = 8 cm

Now it is clear that ca = of + bc

Therefore, point B between A and C.

5. Check that D is the focus of.

Solutions:

As clear in the figure that ad = dg = 3 units.

6. If B is the center ofand C is the center of, Where a, b, c, d in a straight line, say why = cd?

Solutions:

Given

B is the center of AC.

C is the center of vol.Therefore BC = CD (2)

Of (1) and (2)

De = CD is verified

7. Draw five triangles and measure your sides. Verify each if the sum of the lengths on both sides is always smaller than the third page.

Solutions:

Case 1. In triangle ABC

AB = 2,5 cm

BC = 4.8 cm y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y be y y y y y y y y y y y y y y y y y there

CA = 5,2 cm

AB + BC = 2,5 cm + 4,8 cm

= 7,3 cm

AS 7.3> 5.2

∴ AB + BC> AC

Therefore, the sum of two sides of a triangle is larger than the third side.

Case 2. In the PQR triangle

PQ = 2 cm

Qr = 2,5 cm

En = 3.5 less

Pq + qr = 2 cm + 2,5 cm

= 4,5 cm

AS 4.5> 3,5

∴ PQ + QR> PR

Therefore, the sum of two sides of a triangle is larger than the third side.

Autumn 3. In Dreick Xyz

Xy = 5 cm

Yz = 3 cm

Zx = 6,8 cm

Xy + yz = 5 cm + 3 cm

= 8 cm

Like 8> 6.8

∴ xy + yz> zx

Therefore, the sum of two sides of a triangle is larger than the third side.

Autumn 4. In Dreick MNS

Mn = 2.7 cm

Ns = 4 cm

Ms = 4,7 cm

Mn + ns = 2,7 cm + 4 cm

6,7 cm

AS 6.7> 4.7

∴ mn + ns> ms

Therefore, the sum of two sides of a triangle is larger than the third side.

Case 5. In the triangle klm

KL = 3,5 cm

LM = 3,5 cm

Km = 3,5 cm

Kl + lm = 3,5 cm + 3,5 cm

= 7 cm

Como 7 cm> 3.5 cm

∴ KL + LM> km

Therefore, the sum of two sides of a triangle is larger than the third side.

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

Exercise 5.2 Page No. 91

1. What part of a revolution towards the clock needles turns the time of a clock?

(a) 3 a 9

(b) 4 a 7

(c) 7 a 10

(d) 12 a 9

(h) 1 a 10

(f) 6 a 3

Solutions:

We know that the time is in a complete revolution in a 360 schedule⁰

(a) If the hour hand runs towards the 3 to 9 clock needles, it completes 2 angles or 180⁰

∴ Group = 180⁰/ 360⁰

= 1/2

(b) When the hour hand runs towards the 4-7 clock needles, it rotates at the angle of 1 line or 90⁰

∴ Group = 90⁰/ 360⁰

= 1/4

(c) When the hour hand runs towards the 7 to 10 clock needles, it rotates in 1 right angle or 90⁰

∴ Group = 90⁰/ 360⁰

= 1/4

(d) When the hour hand runs toward the clock needles 12 to 9, it completes 3 angles or 270⁰

∴ Group = 270⁰/ 360⁰

= 3/4

(e) When the hand of a watch run towards the clock needles 1 to 10, it makes 3 angles or 270⁰

∴ Group = 270⁰/ 360⁰

= 3/4

(f) When the hour hand runs towards the 6 to 3 clock needles, it completes 3 angles or 270⁰

∴ Group = 270⁰/ 360⁰

= 3/4

2. Where is the hand of a clock stopped when

(a) Do you start in a program at 12 and 1/2 of a revolution?

(b) starts in 2 and 1/2 of a revolution in a schedule?

(C) Does it start in a 5 and 1/4 schedule of a revolution?

(D) Do you start a revolution towards the clock needles at 5 and 3/4?

Solutions:

We know that a complete revolution will be in a schedule, Hand 360⁰

(a) When the hand of one hour of a clock starts at 12 and 1/2 of the revolution towards the clock needles, it rotates in 180⁰.

Therefore, the hand of a clock time to 6 am.

(b) When the time of a clock begins in Revolution 2 and 1/2 towards the clock needles, it rotates in 180⁰

Therefore, the hand of a clock time to 8 am.

(c) When the time of a clock starts at 5 and 1/4 of the revolution towards the clock needles, it rotates in 90⁰

Therefore, the hand of a clock time to 8 am.

(D) When the time hand of a clock starts at 5 and 3/4 of the revolution towards the clock needles, it rotates at 270 in 270⁰

Therefore, the hand of the time of a clock in 2 stops

3. What direction are you exposed when you start?

(a) east and 1/2 of a revolution in a script?

(b) east and 1½ of a revolution in a script?

(C) West and 3/4 to do an anti -hide?

(D) South and make a complete revolution?

(We should indicate this last question on a schedule or anti -hours? Why not?)

Solutions:

If we visit a complete round towards the clock needles or direction in the anti -horary direction, we will enter 360⁰And two neighboring addresses are 90⁰Or 1/4 of a complete revolution of the other.

(a) If we start looking at the east and rotating 1/2 a revolution toward the clock needles, we will be towards the west direction.

(b) If we start looking east and 1½ of a revolution towards the clock needles, we will be west

Em

(D) If we start looking south and make a complete revolution, we will face the south direction.

In the case of the complete revolution of Revolution 1, in a script or in the anti -linch direction, we will return to the original position.

4. What happened to a revolution when you face you?

(a) This and turns into a schedule to face the north?

(b) South and a schedule to face the east

(C) West and deliver a schedule to face the East?

Solutions:

Due to the complete revolution, in a schedule or in the anti -marital direction, we will change around 360⁰And two neighboring addresses are 90⁰or 1/4 of a complete revolution of others

(a) If we stay in the east and turn to face the north

(b) If we start looking south and transforming a program for the East, we have to make 3/4 of a revolution

(c) If we start to stay west and turn to the watches to the east, we have to perform 1/2 of a revolution

5. Find the number of straight angles that were turned by the hand of a watch when released

(a) 3 a 6

(b) 2 a 8

(c) 5 A 11

(d) 10 a 1

(h) 12 a 9

(f) 12 a 6

Solutions:

The hand of a clock is 360⁰Or 4 angles of covering in a complete revolution

(a) If the hand of one hour of a watch is 3 to 6, it rotates in 90⁰The 1 rectal angle

(b) When the hand of one hour of a clock runs from 2 to 8, 180⁰The 2 Falten English

(c) If the hand of one hour of a watch is 5 to 11, 180 spin⁰The 2 Falten English

(D) If the one -hour hand of a clock is 10 to 1, delivery in 90⁰The 1 rectal angle

(e) When the hand of a clock occurs from 12 to 9, it rotates at 270⁰The 3 crase

(f) When the hand of one hour of a clock runs from 12 to 6, 180⁰The 2 Falten English

6. How many straight angles do you do when you start facing?

(a) South and in schedule towards the West?

(b) turn north and in the east times of anti -times times?

(C) Vire West and West?

(D) south and turn north?

Solutions:

If we make a complete round in anti -marard or anti -marard direction, we will enter 360⁰And two neighboring addresses are 90⁰Far from each other.

(a) If we start looking south to the south and turning a schedule toward the west, we have to make a straight angle

(b) When we start looking north and resorting to the east level needles, we have to create 3 straight angles

(C) When we start to stay west and return to the west

(d) When we start with the south and bend the north, we have to create 2 straight angles

7. Where is the time of a watch when it starts?

(a) Turn 6 and 1 right angle?

(b) 8 And it rotates in 2 straight angles?

(C) Turn the angle of 10 and 3 straight angles?

(D) 7 And spin in 2 straight angles?

Solutions:

We know that in 1 complete⁰The 4 blockade

(a) When the time of a clock starts 6 and rotates in 1 right angle, it is stopped at 9

(b) When the time hand of a watch starts 8 and rotates in 2 angles, it stops in 2

(c) When the time of 10 starts at 10 and only rotates in 3 angles, it is interrupted in 7

(d) When the time of a clock starts at 7 and 2 angles, it is stopped at 7

Exercise 5.3 Page No. 94

1. Adjust the following:

(i) right angle (a) less than a quarter of revolution

(ii) right angle (b) more than half of a revolution

(iii) acute angle (c) half of a revolution

(IV) Boring Angle (D) A quarter of a revolution

(v) reflection angle (e) between 1/4 and 1/2 of a revolution

(f) a complete revolution

Solutions:

(I) Juiz Shop = 180⁰Or half of a revolution

Therefore (c) is a correct answer

(ii) Judge Store = 90⁰Or a quarter of a revolution

Therefore (D) is a correct answer

(iii) acute angle = less than 90⁰or less than a quarter of a revolution

So (a) is a correct answer

(IV) Stumpfwinkel = Mais de 90⁰But less than 180⁰or between 1/4 and 1/2 of a revolution

Therefore, a correct answer is (E)

(v) reflection angle = more than 180⁰But less than 360⁰or more than half of a revolution

Therefore (b) is a correct answer

2. Classify each of the following angles as certain, especially acute, frank or reflection:

Solutions:

(i) The offered angle is the acute angle that measures less than 90⁰

(ii) the specified angle is the monotonous angle, as it measures more than 90⁰But less than 180⁰

(iii) the specified angle is the right angle because it measures 90⁰

(IV) The offered angle is the reflex angle because it measures more than 180⁰But less than 360⁰

(v) The specified angle is the right angle because it measures 180⁰

(Vi) the offered angle is an acute angle because it measures less than 90⁰

Exercise 5.4 Page No. 97

1. What is the measure of

(i) a straight angle

(ii) a straight angle

Solutions:

(i) the measure of a straight angle is 90⁰

(ii) the measure of a right angle is 180⁰

2. Say the wrong:

(a) the measure of an acute angle <90⁰

(b) the measure of a forceful angle <90⁰

(c) the measure of a reflex angle> 180⁰

(D) The measure of a complete revolution = 360⁰

(e) Sim, M Professor = 53⁰y M test = 35⁰Then m test m.

Solutions:

(A)It is true that the measure of an acute angle is less than 90⁰

(B) Wrong, the measure of a striking angle is greater than 90⁰But less than 180⁰

(c) The measure of an angle of reflection is greater than 180⁰

(D) correct, the measure of a complete revolution is 360⁰

(E) true, ϩa is greater than zero

3. Write the measures of

(a) some acute angles

(b) some blunt angles

(Enter at least two examples)

Solutions:

(A)The measurements of an acute angle are 50⁰, Sixty-five⁰

(b) The dimensions of the forceful angle are 110⁰175⁰

4. Measure the angles that occur with the provocator below and write the measurement.

Solutions:

(A)The measurement of an angle is 45⁰

(b) the measurement of an angle is 120⁰

(c) the measurement of an angle is 90⁰

(d) the measurements of an angle are 60⁰, 90⁰y 130⁰

5. What angle has a great measure for the first time appreciated and then measures.

Dimension of angle A =

Angle size B =

Solutions:

The measurement of angle A is 40⁰

The measure of angle B is 68⁰

The test has a large measure that

6. From these two angles that have a larger measure? Enjoy and then confirm the measurement.

Solutions:

The measurements of these angles are 45⁰y 55⁰Therefore, the angle shown in the second figure is larger.

7. Perform the empty rooms with a sharp, frank, straightforward or straight:

(a) an angle, whose measure is less than that of a right angle, is _____

(b) an angle, whose size is greater than that of a straight angle ____

(c) an angle, whose measurement is the sum of the dimensions of two straight lines, is _______

(D) If the sum of the dimensions of two angles is that of a straight angle, then each one is _____

(E) If the sum of the two -angle measurements is that of a right angle and one of them is acute, the other must be ______

Solutions:

(A)An angle, whose measurement is less than that of a straight angle, is the acute angle

(b) an angle, whose size is greater than that of a straight angle, is the blunt angle (but less than 180⁰)

(c) an angle, whose measure is the sum of the measurements of two straight lines, is the right angle

(D) If the sum of the two -angle measurements is that of a right angle, each is an acute angle

(E) If the sum of the two -angle measurements is that of a straight angle and one of them is acute, the other should be a blunt angle.

8. Determine the measurement of the angle in all illustrations.

Solutions:

The measurements of the angles shown in the illustration above are 40⁰, 130⁰, Sixty-five⁰y 135⁰

9. Find the measurement of the angle between the hands of the clock in each illustration:

Solutions:

The size of the angle between the hands of the clock is 90⁰, 30⁰y 180⁰

10. Investigation

In the specified illustration, angle 30 measures⁰.Lar of the same figure through a magnifying glass. Is the angle greater? Does the size of the angle change?

Solutions:

The measurement of an angle does not change when you see through a magnifying glass

11. Measure and classify all angles:

Solutions:

Exercise 5.5 Page No. 100

1. Which of the following models are models for vertical lines:

(a) the adjacent edges of a table.

(b) the lines of a railroad.

(C) the line segments that form the letter "L".

(D) The book table v.

Solutions:

(a) The adjacent edges of a table are perpendicular to each other.

(B) The lines of an railroad are parallel to each other.

(c) The line segments that form the letter "L" are perpendicular to each other

(D) The pages of the letter V tend to form an acute angle.

Therefore (A) and (C) are models for vertical lines.

2. SkirtThe segment is perpendicular to the line.To leaveyOverlapping at point A. What is the size of Kaufpay?

Solutions:

The illustration shows that the measure Kaufpay is 90⁰

3. Two squares are defined in your box. What are the measurements of the angles that are formed in your corners? Do you have a common angle measure?

Solutions:

The measurement of the angle at a square of a sentence is 30⁰, 60⁰y 90⁰

The other square established has an angle measure 45⁰, 45⁰y 90⁰

Yes, the measure for measure 90⁰It is common among them

4. Examine the diagram. Line L is perpendicular to the line M

(A) — ES CE = For example?

(b) pe bisect cg?

(C) Identify two popular segments for which PE is the vertical habitder sector.

(D) Are they true?

(i) AC> FG

(ii) CD = gh

(iii) bc <eh.

Solutions:

(a) Yes, since ce = 2 units or z.

(b) yes. CE = for example, because both are 2 units.daí pe -bisect cg

(C)yThey are the line segments, for which PE is the usual vertical sector

(D) (i) true.da AC = 2 units and fg = 1 unit

∴ AC> FG

(ii) true because both are 1 unit

(iii) true.digitis to BC = 1 unit and is = 3 units

∴ bc <eh

Exercise 5.6 Page No. 103

1. Name the types of the following triangles:

(A) Triangle with 7 cm, 8 cm and 9 cm of pages.

(B) ∆ABC CON AB = 8,7 cm, AC = 7 cm y BC = 6 cm.

(c) ∆Pqr tal que pq = qr = pr = 5 cm.

(d) ∆def with heads = 90 °

(e) ∆xyz com ζy = 90 ° e xy = yz.

(f) ∆MN with ζl = 30 °, ζm = 70 ° and test = 80 °.

Solutions:

(a) ScalendCheck

(B) Triangle of scale

(C) balanced triangle

(D) Drophon negligible table angles

(E) Iszelic triangle at the right angle

(f) Acute exhaust triangle

2. Adjust the following:

Triangle triangle measurements

(i) 3 pages with the same length (a) scale

(ii) 2 pages with the same length (B) isken at an angle at an angle

(iii) All sides are different at a blunt angle (C) under different lengths (C)

(IV) 3 acute angles (de) a right angle at the right angle

(V) 1 rectal equilibrium angle (E)

(vi) 1 stump angle (f) acute angle

(Vii) 1 straight angle with two sides of the same length (g) isosceles

Solutions:

(i) balanced triangle

(2) Triangle of Isceles

(iii) scale triangle

(IV) Acute exhaust triangle

(v) only triangle with horny

(Vi) triangle with blunt deformation

(VII) Winkling Verification of Isosceles Rights

3. Name each of the following triangles in two different ways: (You can evaluate the angle type according to observation)

Solutions:

(EU)Acute angular triangle and spatula

(II) Rectangular triangle

(iii) dull hinge triangle

(Iv) legal triangle at angle and isken

(v) triangle at a balanced and sharp angle

.

4. Try to build triangles with game matches. Some are displayed here. You can make a triangle

(a) 3 correspondences?

(b) 4 matches of matches?

(c) 5 correspondences?

(D) 6 matches of matches?

(Remember that you need to use all available correspondence.)

Name the type of triangle. If you can't do a triangle, think about the reasons for that

Solutions:

(A)If we use three correspondences, we can create a triangle as shown below

The anterior triangle is a balanced triangle

(b) When using 4 randoms, we cannot make a triangle because we know that the sum of the lengths of two sides of a triangle is always larger than the third side.

(c) When using 5 randoms, we can make a triangle as shown below

The anterior triangle is an isceles triangle

(D) When using 6 randoms, we can make a triangle as shown below

The anterior triangle is a balanced triangle

Exercise 5.7 Page No. 106

1. Say the Wrong Verdadero:

(a) Each rectangular angle is a straight angle.

(B) The opposite pages of a rectangle are equally long.

(C) The diagonals of a square are perpendicular to each other.

(D) All sides of a rombus are equally long.

(E) All sides of a parallelogram are equally long.

(F) The opposite pages of a trapeze are parallel.

Solutions:

(A) True, every angle of a rectangle is a straight angle

(B) The opposite pages of a rectangle are the same length.

(C) correct, the diagonals of a square are perpendicular

(D) true, all sides of a rombus are equally long

(E) wrong, all sides of a parallelogram are not the same

(f) Wrong, the opposite sides of a trapeze are not parallel

2. Enter the reasons for the following:

(A) You can consider a square as a special rectangle.

(B) A rectangle can be considered a special parallelogram.

(C) You can consider a square as a special rombus.

(D) squares, rectangles, parallelograms are all squares.

(E) The square is also a parallelogram.

Solutions:

(A)A rectangle where all internal angles are equally, ie 90⁰And only the opposite sides of the rectangle are of the same length, while in the square there are all internal angles 90⁰And all sides of the square are the same length. Therefore, a rectangle with all sides becomes a square. Therefore, the square is a special rectangle.

(B) In a parallelogram, the opposite pages are parallel and them. In a rectangle, the opposite pages are parallel and the same. The internal angles of the rectangle are of the same extension, ie 90⁰Therefore, a parallelogram with each angle becomes a straight angle for a square.

(c) All sides of a rombus and square are the same, but in the case of square all internal angles are 90⁰A rombus with each angle when a straight angle becomes a square.

(d) Because everyone is closed and 4 line segments are.

(E) The opposite pages of a parallelogram are the same and in parallel, while in a square the opposite pages are parallel and the 4 sides of the same length are.

3. It is said that a number is regular if its pages are the same and the angles are also in circumference. Can you identify the regular square?

Solutions:

The square is regularly square, as all internal angles are 90⁰And all sides have the same length.

Exercise 5.8 No: 108

1. Examine if the following polygons are. If anyone is not, why?

Solutions:

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

(Ii) is a six -page polygon

(iii) No, it is not a polygon because it does not consist of line segments.

(IV) It is not a polygon because it does not consist of line segments.

2. Name all polygons.

Take two more examples of each of them.

(a) is a closed figure and consists of four line segments.

(b) The specified number is a triangle because it is a closed number with 3 line segments.

(c) The specified number is a pentagon because this closed number consists of 5 line segments.

(d) The specified figure is an octagon because it is a closed figure made of 8 line segments.

3. Draw a hard outline of a normal hexagon. Conecte three of your points -chau, draw a triangle. Identify the type of triangle you designed.

Solutions:

We can draw an isosceles triangle that connects three of the main points of a hexagon, as shown below.

4. Draw an approximate sketch of a normal octagon.

Solution:

The following figure is a regular octagon in which a rectangle is designed by connecting four of the octagon vertex.

5. A diagonal is a line segment that connects two -polygon points and is not one side of the polygon. He draws an approximate sketch of a pentagon and draws his diagonals.

Solutions:

Of the illustration, we can find AC, AD, Bd, Be and CE the diagonals

Exercise 5.9 Page No. 111

1. Adjust the following:

Enter two new examples of each form.

Solutions:

(A)A cone of ice cream and a birthday cap are examples of cones

(B) Cricketball and the tennis ball are examples of sphere

(C) A street roll and a grass roll are examples of cylinders

(D) A book and a brick are examples of cuboids

(E) an Egyptian diamond and pyramid are examples of pyramid

2. What is the way?

(a) Your instrument box?

(B) A brick?

(c) An image of phosphorus?

(D) A street paper?

(E) a sweet day?

Solutions:

(a) The shape of an instrument box is cube

(b) The shape of a brick is the cube

(C) The shape of a matchbox is the cube

(D) The shape of a street roll is the cylinder

(E) The shape of a sweet Laddu is the ball

Issue Responsibility:

Abandoned topic - 5.10 three -dimensional forms.