NCERT Solutions For Class 6 Maths Chapter 14 : Practical Geometry Application

NCERT Maths Book Solutions Class 6 Chapter 14 PDF Free Download

NCERT Solutions For Class 6 Maths Chapter 14 consists of exercise wise solved questions of Practical Geometry topic. These pdf can be downloaded easily and could be used for learning anywhere and at any time. To get an idea of the types of questions asked from Practical Geometry and its weightage in the final exam, students are advised to solve sample papers and previous year question papers as well. NCERT Solutions for Class 6 Chapter 14 Practical Geometry PDF are provided here.

NCERT Solutions for Class 6 Chapter 14: Practical Geometry Download PDF

 

ncert solutions for class 6 maths chapter 14 ex 1
ncert solutions for class 6 maths chapter 14 ex 1
ncert solutions for class 6 maths chapter 14 ex 1
ncert solutions for class 6 maths chapter 14 ex 2
ncert solutions for class 6 maths chapter 14 ex 2
ncert solutions for class 6 maths chapter 14 ex 2
ncert solutions for class 6 maths chapter 14 ex 3
ncert solutions for class 6 maths chapter 14 ex 3
ncert solutions for class 6 maths chapter 14 ex 4
ncert solutions for class 6 maths chapter 14 ex 4
ncert solutions for class 6 maths chapter 14 ex 4
ncert solutions for class 6 maths chapter 14 ex 4
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 5
ncert solutions for class 6 maths chapter 14 ex 6
ncert solutions for class 6 maths chapter 14 ex 6
ncert solutions for class 6 maths chapter 14 ex 6
ncert solutions for class 6 maths chapter 14 ex 6
ncert solutions for class 6 maths chapter 14 ex 6
ncert solutions for class 6 maths chapter 14 ex 6
ncert solutions for class 6 maths chapter 14 ex 6
ncert solutions for class 6 maths chapter 14 ex 6

 

The solutions are available in PDF format which are prepared by our experts, based on the CBSE syllabus, prescribed by the board. Students can also go through the notes and preparation tips available on the website for the preparation of exams.

Exercises of NCERT Solutions Class 6 Maths Chapter 14 – Practical Geometry

Exercise 14.1 Solutions

Exercise 14.2 Solutions

Exercise 14.3 Solutions

Exercise 14.4 Solutions

Exercise 14.5 Solutions

Exercise 14.6 Solutions

Access NCERT Solutions for Class 6 Chapter 14: Practical Geometry

Exercise 14.1 page no: 276

1. Draw a circle of radius 3.2 cm.

Solutions:

The required circle may be drawn as follows:

Step 1: For the required radius 3.2 cm, first open the compasses.

Step 2: For the centre of a circle, mark a point ‘O’.

Step 3: Place a pointer of compasses on ‘O’.

Step 4: Now, turn the compasses slowly to draw the required circle.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 1

2. With the same centre O, draw two circles of radii 4 cm and 2.5 cm.

Solutions:

The required may be drawn as follows:

Step 1: For the required radius 4 cm, first open the compasses

Step 2: For the centre of a circle, mark a point ‘O’

Step 3: Place a pointer of compasses on ‘O’.

Step 4: Turn the compasses slowly to draw the circle.

Step 5: Next, open the compasses for 2.5 cm.

Step 6: Again place a pointer of compasses on ‘O’ and turn the compasses slowly to draw the circle.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 2

3. Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?

Solutions:

We may draw a circle having its centre ‘O’, also of any convenient radius. Let AB and CD be the two diameters of this circle. A quadrilateral is formed when we join the ends of these diameters.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 3

We know that the diameter of a circle are equal in length, hence quadrilateral formed will be having its diagonals of equal length.

Also, OA = OB = OC = OD = radius r and if a quadrilateral has its diagonals of same length bisecting each other. It will be a rectangle.

Let DE and FG be the diameters of the circle such that both are perpendicular to each other. Now we can find that a quadrilateral is formed by joining the ends of these diameters.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 4

We may find that OD = OE = OF = OG = radius r.

In this quadrilateral DFEG, diagonals are equal and perpendicular to each other. Also they are bisecting each other, hence it will be a square.

To check our answers we may measure the length of sides of quadrilateral formed.

 

4. Draw any circle and mark points A, B and C such that

(a) A is on the circle.

(b) B is in the interior of the circle.

(c) C is in the exterior of the circle.

Solutions:

We may draw a circle and three required points A, B, C as follows:

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 5

5. Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 6 and NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 7 are at right angles.

Solutions:

Let us draw two circles having with same radius which are passing through the centre of the other circle.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 8

Here points A and B are the centres of these circles and these circles are intersecting each other at points C and D respectively.

Now in quadrilateral ADBC, we may observe that:

AD = AC [radius of circle centered at A]

BC = BD [radius of circle centered at B]

Since, radiuses of both the circles are equal.

Therefore AD = AC = BC = BD

Hence quadrilateral ADBC is a rhombus and in rhombus diagonals bisect each other at 900. Hence NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 9
and NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.1 - 10
are at right angles.


Exercise 14.2 Page no: 278

1. Draw a line segment of length 7.3 cm using a ruler.

Solutions:

Using a ruler, we can draw a line segment of length 7.3 cm as follows

Step 1: Mark a point A on the sheet

Step 2: Place 0 mark of ruler at point A

Step 3: At 7.3 cm on ruler, mark a point B on the sheet

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 1

Step 4: Now join A and B

Here NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 2
is the required line segment.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 3

2. Construct a line segment of length 5.6 cm using ruler and compasses.

Solutions:

By using a ruler and compasses, we may draw a line segment of length 5.6 cm as follows

Step 1: Draw a line l and mark a point A on this line l.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 4

Step 2: On the zero mark of the ruler, place the compasses. Now extend the compasses to place the pencil up to the 5.6 cm and mark.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 5

Step 3: Place the pointer of compasses on point A and draw an arc to cut l at B. Now, NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 6
is the line segment of 5.6 cm length.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 7

3. Construct NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 8 of length 7.8 cm. From this, cut off NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 9 of length 4.7 cm. Measure NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 10.

Solutions:

Step 1: Draw a line l and mark a point A on it.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 11

Step 2: By adjusting the compasses up to 7.8 cm, while putting the pointer of compasses on point A draw an arc to cut l on B

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 12is the line segment of 7.8 cm

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 13

Step 3: By adjusting the compasses up to 4.7 cm, draw an arc to cut l on C, while putting the pointer of compasses on point A.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 14is the line segment of of 4.7 cm

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 15

Step 4: Now, place the ruler in such a way that 0 mark of the ruler will match with the point C.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 16

Now read the position of point B. It will be 3.1 cm.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 17
is 3.1 cm

 

4. Given NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 18 of length 3.9 cm, construct NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 19 such that the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 20 is twice that of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 21. Verify by measurement.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 22

Solutions:

We can draw a line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 23
such that the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 24
is twice that of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 25
as follows

(1) Draw a line l and mark a point P on it. Let AB be the given line segment of 3.9 cm.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 26

(2) By adjusting the compasses up to the length of AB, place the pointer of compasses at point P and draw an arc to cut the line at X.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 27

(3) Again place the pointer on point X, draw an arc to cut line l at point Q.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 28

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 29
is the required line segment. Using the ruler we may measure the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 30
which comes to 7.8 cm.

5. Given NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 31 of length 7.3 cm and NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 32 of length 3.4 cm, construct a line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 33such that the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 34 is equal to the difference between the lengths of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 35 and NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 36 . Verify by measurement.

Solutions:

(1) Given NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 37
= 7.3 cm and NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 38
= 3.4 cm

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 39

(2) Adjust the compasses up to the length of CD and put the pointer of compasses at point A, draw an arc to cut AB at point P.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 40

(3) Adjust the compasses up to the length of PB. Draw a line l and mark a point X on it.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 41

(4) By placing the pointer of compasses at point X, draw an arc to cut the line at Y.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 42

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 43
is the required line segment

Now, difference between the lengths of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 44
and NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 45
= 7.3 – 3.4

= 3.9 cm

Using the ruler we may measure the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.2 - 46
which comes to 3.9 cm.


Exercise 14.3 page no: 279

1. Draw any line segmentNCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 1. Without measuringNCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 2, construct a copy of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 3.

Solutions:

(1) Let the given line segment be NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 4

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 5

(2) Adjust the compasses up to the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 6

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 7

(3) Draw any line l and mark a point A on it

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 8

(4) Place the pointer on point A, without changing the setting of compasses, draw an arc to cut the line segment at B point.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 9

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 10
is the required line segment

2. Given some line segmentNCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 11, whose length you do not know, construct NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 12 such that the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 13 is twice that of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 14.

Solutions:

Following steps are followed to construct a line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 15
such that the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 16
is twice that of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 17

(1) Let the given line segment be NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 18

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 19

(2) Adjust the compasses up to the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 20

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 21

(3) Draw a line l and mark a point P on it

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 22

(4) Place the pointer on P, draw an arc to cut the line segment at point X, without changing the setting of compasses

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 23

(5) Again with same radius as before, by placing the pointer on point X, draw an arc to cut the line l at point Q

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 24

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.3 - 25is the required line segment.


Exercise 14.4 Page no: 284

1. Draw any line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 1. Mark any point M on it. Through M, draw a perpendicular to NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 2. (use ruler and compasses)

Solutions:

(1) Draw a line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 3
and mark a point M on it.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 4

(2) Taking M as centre and a convenient radius, construct an arc intersecting the line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 5
at points C and D respectively.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 6

(3) By taking centres as C and D and radius greater than CM, construct two arcs such that they intersect each other at point E.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 7

(4) Join EM. Now
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 8is perpendicular to NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 9

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 10

2. Draw any line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 11. Take any point R not on it. Through R, draw a perpendicular to NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 12. (use ruler and set-square)

Solutions:

(1) Draw a given line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 13
and mark a point R outside the line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 14

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 15

(2) Place a set square on NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 16
such that one of its right angles arm aligns along NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 17

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 18

(3) Now, place the ruler along the edge opposite to right angle of set square.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 19

(4) Hold the ruler fixed. Slide the set square along the ruler such that the point R touches the other arm of set square.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 20

(5) Draw a line along this edge of set square which passes through point R. Now, it is the required line perpendicular to NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 21

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 22

 

3. Draw a line l and a point X on it. Through X, draw a line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 23perpendicular to l.

Now draw a perpendicular to XY at Y. (use ruler and compasses)

Solutions:

(1) Draw a line l and mark a point X on it.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 24

(2) By taking X as centre and with a convenient radius, draw an arc intersecting the line l at points A and B respectively.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 25

(3) With A and B as centres and a radius more than AX, construct two arcs such that they intersect each other at point Y.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 26

(4) Join XY. Here NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 27
is perpendicular to l
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 28

Similarly, by taking C and D as centres and radius more than CY, construct two arcs intersecting at point Z. Join ZY. The line
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 29is perpendicular to NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 30
at Y

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.4 - 31


Exercise 14.5 page no: 286

1. Draw
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 1 of length 7.3 cm and find its axis of symmetry.

Solutions:

Following steps are followed to construct
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 2 of length 7.3 cm and to find its axis of symmetry

(1) Draw a line segment
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 3of 7.3 cm

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 4

(2) Take A as centre and draw a circle by using compasses. The radius of circle should be more than half the length of
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 5.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 6

(3) Now, take B as centre and draw another circle using compasses with the same radius as before. Let it cut the previous circle at points C and D

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 7

(4) Join CD. Now
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 8is the axis of symmetry

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 9

2. Draw a line segment of length 9.5 cm and construct its perpendicular bisector.

Solutions:

Following steps are observed to construct a line segment of length 9.5 cm and to construct its perpendicular bisector

(1) Draw a line segment
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 10of 9.5 cm

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 11

(2) Take point P as centre and draw a circle by using compasses. The radius of circle should be more than half the length of
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 12

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 13

(3) Taking the centre at point Q, again draw another circle using compasses with the same radius as before. Let it cut the previous circle at R and S respectively.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 14

(4) Join RS. Now,
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 15is the axis of symmetry i.e the perpendicular bisector of the line
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 16

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 17

 

3. Draw the perpendicular bisector of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 18whose length is 10.3 cm.

(a) Take any point P on the bisector drawn. Examine whether PX = PY.

(b) If M is the mid point of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 19, what can you say about the lengths MX and XY?

Solutions:

(1) Draw a line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 20
of 10.3 cm

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 21

(2) Take point X as centre and draw a circle by using compasses. The radius of circle should be more than half the length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 22

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 23

(3) Now taking Y as centre, draw another circle using compasses with the same radius as before. Let it cut at previous circle at points A and B

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 24

(4) Join AB. Here
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 25is the axis of symmetry

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 26

 

(a) Take any point P on
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 27. We may observe that the measure of lengths of PX and PY are same

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 28being the axis of symmetry, any point lying on
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 29will be at same distance from the both ends of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 30

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 31

(b) M is the midpoint of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 32
. Perpendicular bisector
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 33will be passing through point M. Hence length of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 34
is double of
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 35or 2MX = XY.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 36

4. Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.

Solutions:

(1) Draw a line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 37
of 12.8 cm

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 38

(2) By taking point X as centre and radius more than half of XY, draw a circle.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 39

(3) Again with same radius and centre as Y, draw two arcs to cut the circle at points A and B. Join AB which intersects NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 40
at point M

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 41

(4) By taking X and Y as centres, draw two circles with radius more than half of
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 42

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 43

(5) Taking M as centre and with same radius, draw two arcs to intersect these circles at P, Q and R, S

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 44

(6) Join PQ, and RS. These are intersecting NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 45
at points T and U.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 46

(7) The 4 equal parts of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 47
are
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 48=
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 49=
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 50=
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 51

BY measuring these line segments with the help of a ruler, we may observe that each is of 3.2 cm

5. With NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 52 of length 6.1 cm as diameter, draw a circle.

Solutions:

(1) Draw a line segment NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 53
of 6.1 cm

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 54

(2) Take point P as centre and radius more than half of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 55
, draw a circle

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 56

(3) Again with same radius and Q as centre, draw two arcs intersecting the circle at points R and S

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 57

(4) Join RS which intersects NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 58
at T.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 59

(5) Taking the centre as T and radius TP, draw a circle which passes through Q. Now, this is the required circle.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 60

6. Draw a circle with centre C and radius 3.4 cm. Draw any chord NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 61. Construct the perpendicular bisector of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 62 and examine if it passes through C.

Solutions:

(1) Mark any point C on the sheet

(2) Adjust the compasses up to 3.4 cm and by putting the pointer of compasses at point C, turn compasses slowly to draw the circle. This is the required circle of 3.4 cm radius.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 63

(3) Mark any chord NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 64
in the circle

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 65

(4) Now, taking A and B as centres, draw arcs on both sides of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 66
. Let these intersect each other at points D and E.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 67

(5) Join DE. Now DE is the perpendicular bisector of AB.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 68

If
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 69is extended, it will pass through point C.

7. Repeat Question 6, if NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 70 happens to be a diameter.

Solutions:

(1) Mark any point C on the sheet.

(2) Adjust the compasses up to 3.4 cm and by putting the pointer of compasses at point C, Turn the compasses slowly to draw the circle. This is the required circle of 3.4 cm

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 71

(3) Now mark any diameter NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 72
in the circle.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 73

(4) Now taking A and B as centres, draw arcs on both sides of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 74
with radius more than NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 75
. Let these intersect each other at points D and E.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 76

(5) Join DE, which is perpendicular bisector of AB.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 77

Now, we may observe that
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 78is passing through the centre C of the circle.

8. Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

Solutions:

(1) Mark any point C on the sheet. Now adjust the compasses up to 4 cm and by placing the pointer of compasses at point C, turn the compasses slowly to draw the circle. This is the required circle of 4 cm radius

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 79

(2) Take any two chords NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 80
and
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 81in the circle

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 82

(3) By taking A and B as centres and radius more than half of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 83
, draw arcs on both sides of AB. The arcs are intersecting each other at point E and F. Join EF which is perpendicular bisector of AB.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 84

(4) Again take C and D as centres and radius more than half of
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 85, draw arcs on both sides of CD such that they are intersecting each other at points G, H. Join GH which is perpendicular bisector of CD

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 86

We may observe that when EF and GH are extended they meet at the point O, which is the centre of circle

9. Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 87 and NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 88. Let them meet at P. Is PA = PB?

Solutions:

(1) Draw any angle with vertex as O.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 89

(2) By taking O as centre and with convenient radius, draw arcs on both rays of this angle. Let these points are A and B

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 90

(3) Now take O and A as centres and with radius more than half of OA, draw arcs on both sides of OA. Let these intersects at points C and D respectively. Join CD

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 91

(4) Similarly we may find
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 92which is perpendicular bisector of NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 93
. These perpendicular bisectors
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 94and
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 95intersects each other at point P. Now measure PA and PB. They are equal in length.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 96


Exercise 14.6 page no: 291

1. Draw ∠POQ of measure 75° and find its line of symmetry.

Solutions:

Following steps are followed to construct an angle of 750 and its line of symmetry

(i) Draw a line l and mark two points O and Q on it. Draw an arc of convenient radius, while taking centre as O. Let this intersect line l at R

(ii) Taking R as centre and with same radius as before, draw an arc such that it is intersecting the previously drawn arc at S

(iii) By taking same radius as before and S as centre, draw an arc intersecting the arc at point T as shown in figure

(iv) Take S and T as centre, draw an arc of same radius such that they intersect each other at U

(v) Join OU. Let it intersect the arc at V. Now, take S and V as centres draw arcs with radius more than 1 / 2 SV. Let these intersect each other at P. Join OP. Now OP is the ray making 750 with the line l.

(vi) Let this ray intersect our major arc at point W. By taking R and W as centres, draw arcs with radius more than 1 / 2 RW in the interior angle of 750. Let these intersect each other at point X. Join OX

OX is the line of symmetry for the ∠POQ = 750

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 1

2. Draw an angle of measure 147° and construct its bisector.

Solutions:

Following steps are followed to construct an angle of measure 1470 and its bisector

(i) Draw a line l and mark point O on it. Place the centre of protractor at point O and the zero edge along line l

(ii) Mark a point A at an angle of measure 1470. Join OA. Now OA is the required ray making 1470 with line l

(iii) By taking point O as centre, draw an arc of convenient radius. Let this intersect both rays of angle 1470 at points A and B.

(iv) By taking A and B as centres draw arcs of radius more than 1 / 2 AB in the interior angle of 1470. Let these intersect each other at point C. Join OC.

OC is the required bisector of 1470 angle

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 2

 

3. Draw a right angle and construct its bisector.

Solutions:

Following steps are followed to construct a right angle and its bisector.

(i) Draw a line l and mark a point P on it. Draw an arc of convenient radius by taking point P as centre. Let this intersect line l at R

(ii) Draw an arc by taking R as centre and with the same radius as before such that it is intersecting the previously drawn arc at S

(iii) Take S as centre and with the same radius as before, draw an arc intersecting the arc at T as shown in figure

(iv) By taking S and T as centres draw arcs of same radius such that they are intersecting each other at U.

(v) Join PU. PU is the required ray making a right angle with the line l. Let this intersect major arc at point V.

(vi) Now take R and V as centres, draw arcs with radius more than 1 / 2 RV to intersect each other at point W. Join PW.

PW is the required bisector of this right angle.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 3

 

4. Draw an angle of measure 153° and divide it into four equal parts.

Solutions:

Following steps are followed to construct an angle of measure 1530 and its bisector

(i) Draw a line l and mark a point O on it. Place the centre of protractor at point O and the zero edge along line l

(ii) Mark a point A at the measure of angle 1530. Join OA. Now OA is the required ray making 1530 with line l

(iii) Draw an arc of convenient radius by taking point O as centre. Let this intersects both rays of angle 1530 at points A and B.

(iv) Take A and B as centres and draw arcs of radius more than 1 / 2 AB in the interior of angle of 1530. Let these intersect each other at C. Join OC

(v) Let OC intersect major arc at point D. Draw arcs of radius more than 1 / 2 AD with A and D as centres and also D and B as centres. Let these are intersecting each other at points E and F respectively. Now join OE and OF

OF, OC, OE are the rays dividing 1530 angle into four equal parts.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 4

5. Construct with ruler and compasses, angles of following measures:

(a) 60°

(b) 30°

(c) 90°

(d) 120°

(e) 45°

(f) 135°

Solutions:

(a) 600

Following steps are followed to construct an angle of 600

(i) Draw a line l and mark a point P on it. Take P as centre and with convenient radius, draw an arc of a circle such that it intersects the line l at Q.

(ii) Take Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point R.

(iii) Join PR. PR is the required ray making 600 with the line l.
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 5

(b) 300

Following steps are followed to construct an angle of 300

(i) Draw a line l and mark a point P on it. By taking P as centre and with convenient radius, draw an arc of a circle such that it is intersecting the line l at Q.

(ii) Take Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point R.

(iii) By taking Q and R as centres and with radius more than 1 / 2 RQ draw arcs such that they are intersecting each other at S. Join PS which is the required ray making 300 with the line l.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 6

(c) 900

Following steps are followed to construct an angle of measure 900

(i) Draw a line l and mark a point P on it. Take P as centre and with convenient radius, draw an arc of a circle such that it is intersecting the line l at Q.

(ii) Take Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at R

(iii) By taking R as centre and with the same radius as before, draw an arc intersecting the arc at S as shown in figure

(iv) Now take R and S as centre, draw arc of same radius to intersect each other at T.

(v) Join PT, which is the required ray making 900 with the line l.

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 7

(d) 1200

Following steps are followed to construct an angle of measure 1200

(i) Draw a line l and mark a point P on it. Taking P as centre and with convenient radius, draw an arc of circle such that it is intersecting the line l at Q.

(ii) By taking Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at R.

(iii) Take R as centre and with the same radius as before, draw an arc such that it is intersecting the arc at S as shown in figure.

(iv) Join PS, which is the required ray making 1200 with the line l

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 8

(e) 450

Following steps are followed to construct an angle of measure 450

(i) Draw a line l and mark a point P on it. Take P as centre and with convenient radius, draw an arc of a circle such that it is intersecting the line l at Q.

(ii) Take Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at R

(iii) By taking R as centre and with the same radius as before, draw an arc such that it is intersecting the arc at S as shown in figure.

(iv) Take R and S as centres and draw arcs of same radius such that they are intersecting each other at T

(v) Join PT. Let this intersect the major arc at point U.

(vi) Now take Q and U as centres and draw arcs with radius more than 1 / 2 QU to intersect each other at point V. Join PV.

PV is the required ray making 450 with the line l

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 9

(f) 1350

Following steps are followed to construct an angle of measure 1350

(i) Draw a line l and mark a point P on it. Taking P as centre and with convenient radius, draw a semicircle which intersects the line l at Q and R respectively.

(ii) By taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S

(iii) Taking S as centre and with the same radius as before, draw an arc such that it is intersecting the arc at T as shown in figure

(iv) Take S and T as centres, draw arcs of same radius to intersect each other at U.

(v) Join PU. Let this intersect the arc at V. Now take Q and V as centres and with radius more than 1 / 2 QV, draw arcs to intersects each other at W.

(vi) Join PW which is the required ray making 1350 with the line l

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 10

6. Draw an angle of measure 45° and bisect it.

Solutions:

Following steps are followed to construct an angle of measure 450 and its bisector.

(i) Using the protractor ∠POQ of 450 measure may be formed on a line l

(ii) Draw an arc of convenient radius with centre as O. Let this intersects both rays of angle 450 at points A and B

(iii) Take A and B as centres, draw arcs of radius more than 1 / 2 AB in the interior of angle of 450. Let these intersect each other at C. Join OC

OC is the required bisector of 450 angle

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 11

7. Draw an angle of measure 135° and bisect it.

Solutions:

Following steps are followed to construct an angle of measure 1350 and its bisector.

(i) By using a protractor ∠POQ of 1350 measure may be formed on a line l

(ii) Draw an arc of convenient radius by taking O as centre. Let this intersect both rays of angle 1350 at points A and B respectively.

(iii) Take A and B as centres, draw arcs of radius more than 1 / 2 AB in the interior of angle of 1350. Let these intersect each other at C. Join OC.

OC is the required bisector of 1350 angle

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 12

8. Draw an angle of 700. Make a copy of it using only a straight edge and compasses.

Solutions:

Following steps are followed to construct an angle of measure 700 and its copy.

(i) Draw a line l and mark a point O on it. Now place the centre of protractor at point O and the zero edge along line l.

(ii) Mark a point A at an angle of measure 700. Join OA. Now OA is the ray making 700 with line l. With point O as centre, draw an arc of convenient radius in the interior of 700 angle. Let this intersects both rays of angle 700 at points B and C respectively

(iii) Draw a line m and mark a point P on it. Again draw an arc with same radius as before and P as centre. Let it cut the line m at point D

(iv) Adjust the compasses up to the length of BC. With this radius draw an arc taking D as centre which intersects the previously drawn arc at point E.

(v) Join PE. Here PE is the required ray which makes same angle of measure 700 with the line m

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 13

9. Draw an angle of 400. Copy its supplementary angle.

Solutions:

Following steps are followed to construct an angle of measure 450 and a copy of its supplementary angle

(i) Draw a line segment
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 14and mark a point O on it. Place the centre of protractor at point O and the zero edge along line segment
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 15.

(ii) Mark a point A at an angle of measure 400. Join OA. Here OA is the required ray making 400 with
NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 16. ∠POA is the supplementary angle of 400

(iii) With point O as centre, draw an arc of convenient radius in the interior of ∠POA. Let this intersects both rays of ∠POA at points B and C respectively.

(iv) Draw a line m and mark a point S on it. Again draw an arc by taking S as centre with the same radius as used before. Let it cut the line m at point T.

(v) Now adjust the compasses up to the length of BC. Taking T as centre draw an arc with this radius which will intersect the previously drawn arc at point R.

(vi) Join RS. Here RS is the required ray which makes same angle with the line m, as the supplementary of 400 [i.e 1400]

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.6 - 17


Leave a Comment

Your email address will not be published. Required fields are marked *