NCERT Solutions for Class 6 Maths Practical Geometry [Old Book]
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Page 1
NCERT
SOLUTIONS
CLASS - 6TH
aglase .co
SOLUTIONS
CLASS - 6TH
aglase .co
Page 2
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Class : 6th
Subject : Maths
Chapter : 14
Chapter Name : PRACTICAL GEOMETRY
Exercise 14.1
Q1 Draw a circle of radius 3.2 cm.
Answer. The required circle can be drawn as follows.
step 1
First, open the compasses for the required radius 3.2 cm.
step 2
Mark a point 'O' where we want the centre of the circle to be.
step 3
Place the pointer of compasses on O.
Step 4
Turn the compasses slowly to draw the circle.
Page : 276 , Block Name : Exercise 14.1
Q2 With the same centre O, draw two circles of radii 4 cm and 2.5 cm.
Answer. The required circle can be drawn as follows.
Step 1
First, open the compasses for the required radius 4 cm.
step 2
Mark a point 'O' where we want the centre of the circle to be.
step 3
Place the pointer of compasses on O.
step 4
Turn the compasses slowly to draw the circle.
Page 1 of 27 Aglasem Schools
Class : 6th
Subject : Maths
Chapter : 14
Chapter Name : PRACTICAL GEOMETRY
Exercise 14.1
Q1 Draw a circle of radius 3.2 cm.
Answer. The required circle can be drawn as follows.
step 1
First, open the compasses for the required radius 3.2 cm.
step 2
Mark a point 'O' where we want the centre of the circle to be.
step 3
Place the pointer of compasses on O.
Step 4
Turn the compasses slowly to draw the circle.
Page : 276 , Block Name : Exercise 14.1
Q2 With the same centre O, draw two circles of radii 4 cm and 2.5 cm.
Answer. The required circle can be drawn as follows.
Step 1
First, open the compasses for the required radius 4 cm.
step 2
Mark a point 'O' where we want the centre of the circle to be.
step 3
Place the pointer of compasses on O.
step 4
Turn the compasses slowly to draw the circle.
Page 1 of 27 Aglasem Schools
Page 3
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
step 5
Now, open the compasses for 2.5 cm.
Step 6
Again put the pointer of the compasses on point 'O' and turn the compasses slowly to
draw the circle.
Page : 276 , Block Name : Exercise 14.1
Q3 Draw a circle and any two of its diameters. If you join the ends of these diameters,
what is the �gure obtained? What �gure is obtained if the diameters are perpendicular to
each other? How do you check your answer?
Answer. A circle can be drawn of any convenient radius, also having its centre as O. Let
AB and CD be two diameters of this circle. When we join the ends of these diameters, a
quadrilateral ABCD is formed.
As we know that the diameters of a circle are equal in length, therefore, the quadrilateral
so formed will have its diagonals of equal length.
Also, OA = OB = OC = OD radius r and if a quadrilateral has its diagonals of same
length which are bisecting each other, then it will be a rectangle.
Let DE and FG be two diameters of this circle such that these are perpendicular to each
other. A quadrilateral is formed by joining the ends of these diameters.
Here, OD = OE = OF = OG = radius r
In this quadrilateral DEFG, the diagonals are equal and perpendicular to each other.
Page 2 of 27 Aglasem Schools
step 5
Now, open the compasses for 2.5 cm.
Step 6
Again put the pointer of the compasses on point 'O' and turn the compasses slowly to
draw the circle.
Page : 276 , Block Name : Exercise 14.1
Q3 Draw a circle and any two of its diameters. If you join the ends of these diameters,
what is the �gure obtained? What �gure is obtained if the diameters are perpendicular to
each other? How do you check your answer?
Answer. A circle can be drawn of any convenient radius, also having its centre as O. Let
AB and CD be two diameters of this circle. When we join the ends of these diameters, a
quadrilateral ABCD is formed.
As we know that the diameters of a circle are equal in length, therefore, the quadrilateral
so formed will have its diagonals of equal length.
Also, OA = OB = OC = OD radius r and if a quadrilateral has its diagonals of same
length which are bisecting each other, then it will be a rectangle.
Let DE and FG be two diameters of this circle such that these are perpendicular to each
other. A quadrilateral is formed by joining the ends of these diameters.
Here, OD = OE = OF = OG = radius r
In this quadrilateral DEFG, the diagonals are equal and perpendicular to each other.
Page 2 of 27 Aglasem Schools
Page 4
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Also, since these are bisecting each other, it will be a square. The length of the sides of
the quadrilateral so formed can be measured to check our answers.
Page : 276 , Block Name : Exercise 14.1
Q4 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.
Answer. A circle and three required points A, B, C can be drawn as follows.
Page : 276 , Block Name : Exercise 14.1
Q5 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 AB and CD are at right angles.
Answer. Let us draw two circles of same radius which are passing through the centres of
the other circle.
Here, point A and B are the centres Of these circles and these circles are intersecting
each other at point c and O.
In quadrilateral ADBC,
AD = AC (Radius of circle centered at A)
BC = BD (Radius of circle centered at B)
As radius of both circles are equal, therefore, AD = AC = BC = BD
Hence, ADBC is a rhombus and i an rhombus, the diagonals bisect each other at 90∘ .
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Hence, AB and CD are at right angles.
Page : 276 , Block Name : Exercise 14.1
Page 3 of 27 Aglasem Schools
Also, since these are bisecting each other, it will be a square. The length of the sides of
the quadrilateral so formed can be measured to check our answers.
Page : 276 , Block Name : Exercise 14.1
Q4 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.
Answer. A circle and three required points A, B, C can be drawn as follows.
Page : 276 , Block Name : Exercise 14.1
Q5 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 AB and CD are at right angles.
Answer. Let us draw two circles of same radius which are passing through the centres of
the other circle.
Here, point A and B are the centres Of these circles and these circles are intersecting
each other at point c and O.
In quadrilateral ADBC,
AD = AC (Radius of circle centered at A)
BC = BD (Radius of circle centered at B)
As radius of both circles are equal, therefore, AD = AC = BC = BD
Hence, ADBC is a rhombus and i an rhombus, the diagonals bisect each other at 90∘ .
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Hence, AB and CD are at right angles.
Page : 276 , Block Name : Exercise 14.1
Page 3 of 27 Aglasem Schools
Page 5
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Exercise 14.2
Q1 Draw a line segment of length 7.3 cm using a ruler.
Answer. A line segment of length 7.3 cm can be drawn using a ruler as follows.
(1) Mark a point A on the sheet.
(2) Put O mark of ruler at point A.
(3) Mark a point B on the sheet at 7.3 cm on ruler.
(4) Join A and B.
¯¯¯¯¯¯¯¯
AB is the required line segment
Page : 278 , Block Name : Exercise 14.2
Q2 Construct a line segment of length 5.6 cm using ruler and compasses.
Answer. A line segment of length 5.6 cm can be drawn using using a ruler and compasses
as follows.
(1) Draw a line l and mark a point A on this line.
(2) Place the compasses on the zero mark of the ruler. Open it to place the pencil up to
5.6 cm mark.
(3) Place the pointer of compasses on point A and draw an arc to cut l at B. AB is the line
segment of 5.6 cm length.
Page : 278 , Block Name : Exercise 14.2
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q3 Construct AB of length 7.8 cm. From this, cut off AC of length 4.7 cm. Measure BC.
Page 4 of 27 Aglasem Schools
Exercise 14.2
Q1 Draw a line segment of length 7.3 cm using a ruler.
Answer. A line segment of length 7.3 cm can be drawn using a ruler as follows.
(1) Mark a point A on the sheet.
(2) Put O mark of ruler at point A.
(3) Mark a point B on the sheet at 7.3 cm on ruler.
(4) Join A and B.
¯¯¯¯¯¯¯¯
AB is the required line segment
Page : 278 , Block Name : Exercise 14.2
Q2 Construct a line segment of length 5.6 cm using ruler and compasses.
Answer. A line segment of length 5.6 cm can be drawn using using a ruler and compasses
as follows.
(1) Draw a line l and mark a point A on this line.
(2) Place the compasses on the zero mark of the ruler. Open it to place the pencil up to
5.6 cm mark.
(3) Place the pointer of compasses on point A and draw an arc to cut l at B. AB is the line
segment of 5.6 cm length.
Page : 278 , Block Name : Exercise 14.2
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q3 Construct AB of length 7.8 cm. From this, cut off AC of length 4.7 cm. Measure BC.
Page 4 of 27 Aglasem Schools
Page 6
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Answer.
Page : 278 , Block Name : Exercise 14.2
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q4 Given AB of length 3.9 cm, construct PQ such that the length of PQ is twice that of
¯¯¯¯¯¯¯¯
AB. Verify by measurement.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(Hint : Construct PX such that length of PX = length of AB; then cut off XQ such that
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
XQ also has the length of AB.)
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Answer. A line segment PQ can be drawn such that the length of PQ is twice that of AB
as follows.
(1) Draw a line l and mark a point P on it and let AB be the given line segment of 3.9 cm.
(2) By adjusting the compasses up to the length of AB, draw an arc to cut the line at X,
while taking the pointer of compasses at point P.
(3) Again put the pointer on point X and draw an arc to cut line l again at Q.
Page 5 of 27 Aglasem Schools
Answer.
Page : 278 , Block Name : Exercise 14.2
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q4 Given AB of length 3.9 cm, construct PQ such that the length of PQ is twice that of
¯¯¯¯¯¯¯¯
AB. Verify by measurement.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(Hint : Construct PX such that length of PX = length of AB; then cut off XQ such that
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
XQ also has the length of AB.)
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Answer. A line segment PQ can be drawn such that the length of PQ is twice that of AB
as follows.
(1) Draw a line l and mark a point P on it and let AB be the given line segment of 3.9 cm.
(2) By adjusting the compasses up to the length of AB, draw an arc to cut the line at X,
while taking the pointer of compasses at point P.
(3) Again put the pointer on point X and draw an arc to cut line l again at Q.
Page 5 of 27 Aglasem Schools
Page 7
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
PQ is the required line segment. By ruler, the length of PQ can be measured which
comes to 7.8 cm.
Page : 278 , Block Name : Exercise 14.2
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q5 Given AB of length 7.3 cm and CD of length 3.4 cm, construct a line segment XY
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
such that the length of XY is equal to the difference between the lengths of AB and CD
. Verify by measurement.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Answer. (1) Given that, AB = 7.3 cm and CD = 3.4 cm
(2) Adjust the compasses up to the length of CD and put the pointer of the compasses at
A. Draw an arc to cut AB at P.
(3) Adjust the compasses up to the length of PB. Now draw a line l and mark a point X on
it.
(4) Now, putting the pointer of compasses at point X, draw an arc to cut the line at Y.
¯¯¯¯¯¯¯¯
XY is the required line segment.
Page : 278 , Block Name : Exercise 14.2
Exercise 14.3
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q1 Draw any line segment PQ. Without measuring PQ, construct a copy of PQ.
Answer.
Page 6 of 27 Aglasem Schools
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
PQ is the required line segment. By ruler, the length of PQ can be measured which
comes to 7.8 cm.
Page : 278 , Block Name : Exercise 14.2
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q5 Given AB of length 7.3 cm and CD of length 3.4 cm, construct a line segment XY
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
such that the length of XY is equal to the difference between the lengths of AB and CD
. Verify by measurement.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Answer. (1) Given that, AB = 7.3 cm and CD = 3.4 cm
(2) Adjust the compasses up to the length of CD and put the pointer of the compasses at
A. Draw an arc to cut AB at P.
(3) Adjust the compasses up to the length of PB. Now draw a line l and mark a point X on
it.
(4) Now, putting the pointer of compasses at point X, draw an arc to cut the line at Y.
¯¯¯¯¯¯¯¯
XY is the required line segment.
Page : 278 , Block Name : Exercise 14.2
Exercise 14.3
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q1 Draw any line segment PQ. Without measuring PQ, construct a copy of PQ.
Answer.
Page 6 of 27 Aglasem Schools
Page 8
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 279 , Block Name : Exercise 14.3
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q2 Given some line segment AB, whose length you do not know, construct PQ such
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
that the length of PQ is twice that of AB.
Answer.
Page 7 of 27 Aglasem Schools
Page : 279 , Block Name : Exercise 14.3
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q2 Given some line segment AB, whose length you do not know, construct PQ such
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
that the length of PQ is twice that of AB.
Answer.
Page 7 of 27 Aglasem Schools
Page 9
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 279 , Block Name : Exercise 14.3
Exercise 14.4
¯¯¯¯¯¯¯¯
Q1 Draw any line segment AB. Mark any point M on it. Through M, draw a
¯¯¯¯¯¯¯¯
perpendicular to AB. (use ruler and compasses)
Answer.
Page 8 of 27 Aglasem Schools
Page : 279 , Block Name : Exercise 14.3
Exercise 14.4
¯¯¯¯¯¯¯¯
Q1 Draw any line segment AB. Mark any point M on it. Through M, draw a
¯¯¯¯¯¯¯¯
perpendicular to AB. (use ruler and compasses)
Answer.
Page 8 of 27 Aglasem Schools
Page 10
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 284 , Block Name : Exercise 14.4
¯¯¯¯¯¯¯¯
Q2 Draw any line segment PQ . Take any point R not on it. Through R, draw a
¯¯¯¯¯¯¯¯
perpendicular to PQ . (use ruler and set-square).
Answer.
Page 9 of 27 Aglasem Schools
Page : 284 , Block Name : Exercise 14.4
¯¯¯¯¯¯¯¯
Q2 Draw any line segment PQ . Take any point R not on it. Through R, draw a
¯¯¯¯¯¯¯¯
perpendicular to PQ . (use ruler and set-square).
Answer.
Page 9 of 27 Aglasem Schools
Page 11
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page 10 of 27 Aglasem Schools
Page 10 of 27 Aglasem Schools
Page 12
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 284 , Block Name : Exercise 14.4
¯¯¯¯¯¯¯¯
Q3 Draw a line l and a point X on it. Through X, draw a line segment XY perpendicular
to l.
¯¯¯¯¯¯¯¯
Now draw a perpendicular to XY at Y. (use ruler and compasses).
Answer.
Page : 284 , Block Name : Exercise 14.4
Exercise 14.5
¯¯¯¯¯¯¯¯
Q1 Draw AB of length 7.3 cm and �nd its axis of symmetry.
Answer.
Page 11 of 27 Aglasem Schools
Page : 284 , Block Name : Exercise 14.4
¯¯¯¯¯¯¯¯
Q3 Draw a line l and a point X on it. Through X, draw a line segment XY perpendicular
to l.
¯¯¯¯¯¯¯¯
Now draw a perpendicular to XY at Y. (use ruler and compasses).
Answer.
Page : 284 , Block Name : Exercise 14.4
Exercise 14.5
¯¯¯¯¯¯¯¯
Q1 Draw AB of length 7.3 cm and �nd its axis of symmetry.
Answer.
Page 11 of 27 Aglasem Schools
Page 13
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 286 , Block Name : Exercise 14.5
Q2 Draw a line segment of length 9.5 cm and construct its perpendicular bisector.
Answer.
Page 12 of 27 Aglasem Schools
Page : 286 , Block Name : Exercise 14.5
Q2 Draw a line segment of length 9.5 cm and construct its perpendicular bisector.
Answer.
Page 12 of 27 Aglasem Schools
Page 14
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 286 , Block Name : Exercise 14.5
¯¯¯¯¯¯¯¯
Q3 Draw the perpendicular bisector of XY whose 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 XY , what
can you say about the lengths MX and XY?
Answer.
Page 13 of 27 Aglasem Schools
Page : 286 , Block Name : Exercise 14.5
¯¯¯¯¯¯¯¯
Q3 Draw the perpendicular bisector of XY whose 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 XY , what
can you say about the lengths MX and XY?
Answer.
Page 13 of 27 Aglasem Schools
Page 15
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 286 , Block Name : Exercise 14.5
Q4 Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal
parts. Verify by actual measurement.
Answer.
Page 14 of 27 Aglasem Schools
Page : 286 , Block Name : Exercise 14.5
Q4 Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal
parts. Verify by actual measurement.
Answer.
Page 14 of 27 Aglasem Schools
Page 16
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 286 , Block Name : Exercise 14.5
Page 15 of 27 Aglasem Schools
Page : 286 , Block Name : Exercise 14.5
Page 15 of 27 Aglasem Schools
Page 17
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
¯¯¯¯¯¯¯¯
Q5 With PQ of length 6.1 cm as diameter, draw a circle.
Answer.
Page 16 of 27 Aglasem Schools
¯¯¯¯¯¯¯¯
Q5 With PQ of length 6.1 cm as diameter, draw a circle.
Answer.
Page 16 of 27 Aglasem Schools
Page 18
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 286 , Block Name : Exercise 14.5
¯¯¯¯¯¯¯¯
Q6 Draw a circle with centre C and radius 3.4 cm. Draw any chord AB. Construct the
¯¯¯¯¯¯¯¯
perpendicular bisector of AB and examine if it passes through C.
Answer.
Page : 286 , Block Name : Exercise 14.5
¯¯¯¯¯¯¯¯
Q7 Repeat Question 6, if AB happens to be a diameter.
Page 17 of 27 Aglasem Schools
Page : 286 , Block Name : Exercise 14.5
¯¯¯¯¯¯¯¯
Q6 Draw a circle with centre C and radius 3.4 cm. Draw any chord AB. Construct the
¯¯¯¯¯¯¯¯
perpendicular bisector of AB and examine if it passes through C.
Answer.
Page : 286 , Block Name : Exercise 14.5
¯¯¯¯¯¯¯¯
Q7 Repeat Question 6, if AB happens to be a diameter.
Page 17 of 27 Aglasem Schools
Page 19
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Answer.
Page : 286 , Block Name : Exercise 14.5
Q8 Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular
bisectors of these chords. Where do they meet?
Answer.
Page 18 of 27 Aglasem Schools
Answer.
Page : 286 , Block Name : Exercise 14.5
Q8 Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular
bisectors of these chords. Where do they meet?
Answer.
Page 18 of 27 Aglasem Schools
Page 20
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 286 , Block Name : Exercise 14.5
Q9 . 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 OA and OB. Let them meet at P.
Is PA = PB ?
Answer.
Page 19 of 27 Aglasem Schools
Page : 286 , Block Name : Exercise 14.5
Q9 . 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 OA and OB. Let them meet at P.
Is PA = PB ?
Answer.
Page 19 of 27 Aglasem Schools
Page 21
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 286 , Block Name : Exercise 14.5
Page 20 of 27 Aglasem Schools
Page : 286 , Block Name : Exercise 14.5
Page 20 of 27 Aglasem Schools
Page 22
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Exercise 14.6
Q1 Draw ∠POQ of measure 75∘ and �nd its line of symmetry.
Answer. DIY
Page : 291 , Block Name : Exercise 14.6
Q2 Draw an angle of measure 147∘ and construct its bisector.
Answer. The below given steps will be followed to construct an angle of 147∘ measure
and its bisector.
(1) Draw a line l and mark a point O on it. Place the centre of the protractor at point O
and the zero edge along line l.
(2) Mark a point A at 147∘ . JoinOA. OA is the required ray making 147∘ with line l.
(3) Draw an arc of convenient radius, while taking point O as center. Let it intersect both
rays of angle 147∘ at point A and B.
(4) Taking A and B as centres, draw arc of radius more than 1/2 AB in the interior of
angle of 147∘ .Let those intersect each other at C. Join OC.
OC is the required bisector of 147∘ angle.
Page : 291 , Block Name : Exercise 14.6
Q3 Draw a right angle and construct its bisector.
Answer. The below given steps will be followed to construct a right angle and its bisector.
(1) Draw a line l and mark a point P on it. Draw an arc of convenient radius, while taking
point P as centre. Let it intersect line I at R.
(2) Taking R as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at S.
(3) Taking s as centre and With the same radius as before, draw an arc intersecting the
arc at T (see �gure).
Page 21 of 27 Aglasem Schools
Exercise 14.6
Q1 Draw ∠POQ of measure 75∘ and �nd its line of symmetry.
Answer. DIY
Page : 291 , Block Name : Exercise 14.6
Q2 Draw an angle of measure 147∘ and construct its bisector.
Answer. The below given steps will be followed to construct an angle of 147∘ measure
and its bisector.
(1) Draw a line l and mark a point O on it. Place the centre of the protractor at point O
and the zero edge along line l.
(2) Mark a point A at 147∘ . JoinOA. OA is the required ray making 147∘ with line l.
(3) Draw an arc of convenient radius, while taking point O as center. Let it intersect both
rays of angle 147∘ at point A and B.
(4) Taking A and B as centres, draw arc of radius more than 1/2 AB in the interior of
angle of 147∘ .Let those intersect each other at C. Join OC.
OC is the required bisector of 147∘ angle.
Page : 291 , Block Name : Exercise 14.6
Q3 Draw a right angle and construct its bisector.
Answer. The below given steps will be followed to construct a right angle and its bisector.
(1) Draw a line l and mark a point P on it. Draw an arc of convenient radius, while taking
point P as centre. Let it intersect line I at R.
(2) Taking R as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at S.
(3) Taking s as centre and With the same radius as before, draw an arc intersecting the
arc at T (see �gure).
Page 21 of 27 Aglasem Schools
Page 23
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
(4) Taking S and T as Centres, draw arcs of same radius to intersect each Other at U.
(5) Join PU. PU is the required ray making 900 with line l. Let it intersect the major arc
at point V.
(6) Now, taking R and V as centres, draw arcs With radius more than 1/2 RV to intersect
each Other at W. Join PW.
PW is the required bisector of this right angle.
Page : 291 , Block Name : Exercise 14.6
Q4 Draw an angle of measure 153∘ and divide it into four equal parts.
Answer. The below given steps will be followed to construct an angle of 153∘ measure
and its bisector.
(1) Draw a line I and mark a point O on it. Place the centre of the protractor at point O
and the zero edge along line l.
(2) Mark a point A at 153∘ . Join OA. OA is the required ray making 153∘ with line l.
(3) Draw an arc Of convenient radius, While taking point O as centre. Let it intersect
both rays Of angle 153∘ at point A and B.
(4) Taking A and B as centres, draw arcs of radius more than 1/2 AB in the interior of
angle of 153∘ . Let those Intersect each other at C. join OC.
(5) Let OC intersect the major arc at point D. Now, with radius more than 1/2 AD, draw
arcs while taking A and O as centres, and D and B as centres. Let these be intersecting
each other at point E and F respectively. Join OE, OF. OF, OC, OE are the rays dividing
153∘ angle in 4 equal parts.
Page 22 of 27 Aglasem Schools
(4) Taking S and T as Centres, draw arcs of same radius to intersect each Other at U.
(5) Join PU. PU is the required ray making 900 with line l. Let it intersect the major arc
at point V.
(6) Now, taking R and V as centres, draw arcs With radius more than 1/2 RV to intersect
each Other at W. Join PW.
PW is the required bisector of this right angle.
Page : 291 , Block Name : Exercise 14.6
Q4 Draw an angle of measure 153∘ and divide it into four equal parts.
Answer. The below given steps will be followed to construct an angle of 153∘ measure
and its bisector.
(1) Draw a line I and mark a point O on it. Place the centre of the protractor at point O
and the zero edge along line l.
(2) Mark a point A at 153∘ . Join OA. OA is the required ray making 153∘ with line l.
(3) Draw an arc Of convenient radius, While taking point O as centre. Let it intersect
both rays Of angle 153∘ at point A and B.
(4) Taking A and B as centres, draw arcs of radius more than 1/2 AB in the interior of
angle of 153∘ . Let those Intersect each other at C. join OC.
(5) Let OC intersect the major arc at point D. Now, with radius more than 1/2 AD, draw
arcs while taking A and O as centres, and D and B as centres. Let these be intersecting
each other at point E and F respectively. Join OE, OF. OF, OC, OE are the rays dividing
153∘ angle in 4 equal parts.
Page 22 of 27 Aglasem Schools
Page 24
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 291 , Block Name : Exercise 14.6
Q5 Construct with ruler and compasses, angles of following measures:
(a) 60∘
(b) 30∘
(c) 90∘
(d) 120∘
(e) 45∘
(f) 135∘
Answer. (a) 60∘
The below given steps will be followed to construct an angle of 60∘ .
(1) Draw a line l and mark a point P on it. Now, taking P as centre and with a convenient
radius, draw an arc of a circle which intersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at point R.
(3) Join PR Which iS the required ray making 60∘ With line l.
(b) 30∘
The below given steps will be followed to construct an angle of 30∘ .
(1) Draw a line l and mark a point p on it. NOW taking p as centre and With convenient
radius, draw an arc of a circle which intersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at point R.
(3) Now, taking Q and R as centre and with radius more than 2 RQ, draw arcs to
intersect each other at S. Join PS which is the required ray making 30∘ with line l.
(c) 90∘
Page 23 of 27 Aglasem Schools
Page : 291 , Block Name : Exercise 14.6
Q5 Construct with ruler and compasses, angles of following measures:
(a) 60∘
(b) 30∘
(c) 90∘
(d) 120∘
(e) 45∘
(f) 135∘
Answer. (a) 60∘
The below given steps will be followed to construct an angle of 60∘ .
(1) Draw a line l and mark a point P on it. Now, taking P as centre and with a convenient
radius, draw an arc of a circle which intersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at point R.
(3) Join PR Which iS the required ray making 60∘ With line l.
(b) 30∘
The below given steps will be followed to construct an angle of 30∘ .
(1) Draw a line l and mark a point p on it. NOW taking p as centre and With convenient
radius, draw an arc of a circle which intersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at point R.
(3) Now, taking Q and R as centre and with radius more than 2 RQ, draw arcs to
intersect each other at S. Join PS which is the required ray making 30∘ with line l.
(c) 90∘
Page 23 of 27 Aglasem Schools
Page 25
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
The below given steps will be followed to construct an angle of 90∘ .
(1) a line l and mark a point p on it. NOW taking p as centre and with a convenient
radius, draw an arc of a circle which intersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw an arc intersecting the
arc at S (see �gure).
(4) Taking R and S as centre, draw an arc of same radius to intersect each other at T.
(5) Join PT. which is the required ray making 90∘ with line l.
(d) 120∘
The below given Steps Will be followed to construct an angle Of 120∘ .
(1) Draw a line l and mark( a point P on it. Now taking P as centre and with a convenient
radius, draw an arc of a circle which intersects line at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw an arc intersecting the
arc at S (see �gure).
(4) Join PS, which is the required ray making 120∘ with line l.
(e) 45∘
The below given steps will be followed to construct an angle of 45∘ .
(1) Draw a line l and mark a point P on it. Now taking P as centre and with a convenient
radius, draw an arc of a circle which intersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw an arc intersecting the
arc at S (see �gure).
(4) Taking R and s as centres, draw arcs Of same radius to intersect each Other at T.
Page 24 of 27 Aglasem Schools
The below given steps will be followed to construct an angle of 90∘ .
(1) a line l and mark a point p on it. NOW taking p as centre and with a convenient
radius, draw an arc of a circle which intersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw an arc intersecting the
arc at S (see �gure).
(4) Taking R and S as centre, draw an arc of same radius to intersect each other at T.
(5) Join PT. which is the required ray making 90∘ with line l.
(d) 120∘
The below given Steps Will be followed to construct an angle Of 120∘ .
(1) Draw a line l and mark( a point P on it. Now taking P as centre and with a convenient
radius, draw an arc of a circle which intersects line at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw an arc intersecting the
arc at S (see �gure).
(4) Join PS, which is the required ray making 120∘ with line l.
(e) 45∘
The below given steps will be followed to construct an angle of 45∘ .
(1) Draw a line l and mark a point P on it. Now taking P as centre and with a convenient
radius, draw an arc of a circle which intersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw an arc intersecting the
arc at S (see �gure).
(4) Taking R and s as centres, draw arcs Of same radius to intersect each Other at T.
Page 24 of 27 Aglasem Schools
Page 26
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
(5) Join PT. Let it intersect the major arc at point U.
(6) Taking Q and as centres, draw arcs With radius more than 1/2 QU to intersect each
other at V. Join PV. PV is the required ray making 45∘ With the given line l.
(f) 135∘
The below given steps will be followed to construct an angle of 135∘ .
(1) Draw a line and mark a point P on it. Now taking P as centre and with a convenient
radius, draw a semi-circle which intersects line l at Q and R.
(2) Taking R as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at S.
(3) Taking S as centre and with the same radius as before, draw an arc intetsecting the
arc at T (see �gure).
(4) Taking S and T as centre, draw arcs of same radius to intersect each other at U.
(5) Join PU. Let it intersect the arc at V. NOW taking Q and V as centres and With radius
more than 2 QV, draw arcs to intersect each other at W.
(6) Join PW Which iS the required ray making 135∘ With line
Page : 291 , Block Name : Exercise 14.6
Q6 Draw an angle of measure 45∘ and bisect it.
Answer. DIY
Page : 291 , Block Name : Exercise 14.6
Q7 Draw an angle of measure 135∘ and bisect it.
Page 25 of 27 Aglasem Schools
(5) Join PT. Let it intersect the major arc at point U.
(6) Taking Q and as centres, draw arcs With radius more than 1/2 QU to intersect each
other at V. Join PV. PV is the required ray making 45∘ With the given line l.
(f) 135∘
The below given steps will be followed to construct an angle of 135∘ .
(1) Draw a line and mark a point P on it. Now taking P as centre and with a convenient
radius, draw a semi-circle which intersects line l at Q and R.
(2) Taking R as centre and with the same radius as before, draw an arc intersecting the
previously drawn arc at S.
(3) Taking S as centre and with the same radius as before, draw an arc intetsecting the
arc at T (see �gure).
(4) Taking S and T as centre, draw arcs of same radius to intersect each other at U.
(5) Join PU. Let it intersect the arc at V. NOW taking Q and V as centres and With radius
more than 2 QV, draw arcs to intersect each other at W.
(6) Join PW Which iS the required ray making 135∘ With line
Page : 291 , Block Name : Exercise 14.6
Q6 Draw an angle of measure 45∘ and bisect it.
Answer. DIY
Page : 291 , Block Name : Exercise 14.6
Q7 Draw an angle of measure 135∘ and bisect it.
Page 25 of 27 Aglasem Schools
Page 27
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Answer. The below given steps will be followed to construct an angle of 135∘ and its
bisector.
(1) DPOQ of 135∘ measure can be formed on a line I by using the protractor.
(2) Draw an arc of a convenient radius, while taking point O as centre. Let it intersect
both rays Of angle 135∘ at point A and B.
(3) Taking A and B as centres, draw arcs Of radius more than 1/2 AB in the interior of
angle of 135∘ . Let those intersect each other at c. Join OC.
OC is the required bisector of 135∘ angle.
Page : 291 , Block Name : Exercise 14.6
Q8 Draw an angle of 70∘ . Make a copy of it using only a straight edge and compasses.
Answer. The below given steps will be followed to construct an angle of 70∘ measure and
its
copy.
(1) Draw a line I and mark a point O on it. Place the centre of the protractor at point O
and the zero edge along line l.
(2) Mark a point A at 70∘ . Join OA. OA is the ray making 70∘ with line l. Draw an arc of
convenient radius in the interior of 70∘ angle, while taking point O as centre. Let it
intersect both rays of angle 70∘ at point B and C.
(3) Draw a line m and mark a point P on it. With the same radius as used before, again
draw an arc while taking point P as centre. Let it cut the line m at point D.
(4) Now, adjust the compasses up to the length of With this radius, draw an arc
while taking D as centre, which will intersect the previously drawn arc at point E.
(5) Join PE. PE is the required ray which makes the same angle (i.e. 70∘ ) with line m.
Page 26 of 27 Aglasem Schools
Answer. The below given steps will be followed to construct an angle of 135∘ and its
bisector.
(1) DPOQ of 135∘ measure can be formed on a line I by using the protractor.
(2) Draw an arc of a convenient radius, while taking point O as centre. Let it intersect
both rays Of angle 135∘ at point A and B.
(3) Taking A and B as centres, draw arcs Of radius more than 1/2 AB in the interior of
angle of 135∘ . Let those intersect each other at c. Join OC.
OC is the required bisector of 135∘ angle.
Page : 291 , Block Name : Exercise 14.6
Q8 Draw an angle of 70∘ . Make a copy of it using only a straight edge and compasses.
Answer. The below given steps will be followed to construct an angle of 70∘ measure and
its
copy.
(1) Draw a line I and mark a point O on it. Place the centre of the protractor at point O
and the zero edge along line l.
(2) Mark a point A at 70∘ . Join OA. OA is the ray making 70∘ with line l. Draw an arc of
convenient radius in the interior of 70∘ angle, while taking point O as centre. Let it
intersect both rays of angle 70∘ at point B and C.
(3) Draw a line m and mark a point P on it. With the same radius as used before, again
draw an arc while taking point P as centre. Let it cut the line m at point D.
(4) Now, adjust the compasses up to the length of With this radius, draw an arc
while taking D as centre, which will intersect the previously drawn arc at point E.
(5) Join PE. PE is the required ray which makes the same angle (i.e. 70∘ ) with line m.
Page 26 of 27 Aglasem Schools
Page 28
Book: Mathematics NCERT Solutions | Chapter - 14 Maths
Page : 291 , Block Name : Exercise 14.6
Q9 Draw an angle of 40∘ . Copy its supplementary angle.
Answer. The below given steps will be followed to construct an angle of 40∘ measure and
the copy of Its supplementary angle.
¯¯¯¯¯¯¯¯
(1) Draw a line segment PQ and mark a point O on it. place the centre of the protractor
¯¯¯¯¯¯¯¯
at point O and the zero edge along line segment PQ.
¯¯¯¯¯¯¯¯
(2) Mark a point A at 40∘ . Join OA. OA is the required ray making 40∘ with PQ. D POA is
the supplementary angle of 40∘ .
(3) Draw an arc of convenient radius in the interior of D POA, while taking point O as
centre. Let it both rays of D POA at point B and C.
(4) Draw a line m and mark a point S on it. With the same radius as used before, again
draw an arc while taking point S as centre. Let it cut the line m at point T.
(5) Now, adjust the compasses up to the length of BC. With this radius, draw an arc
while taking T as centre, which will intersect the previously drawn arc at point R.
(6) Join RS. RS is the required ray which makes the same angle with line m, as the
supplementary of 40∘ is 140∘ .
Page : 291 , Block Name : Exercise 14.6
Page 27 of 27 Aglasem Schools
Page : 291 , Block Name : Exercise 14.6
Q9 Draw an angle of 40∘ . Copy its supplementary angle.
Answer. The below given steps will be followed to construct an angle of 40∘ measure and
the copy of Its supplementary angle.
¯¯¯¯¯¯¯¯
(1) Draw a line segment PQ and mark a point O on it. place the centre of the protractor
¯¯¯¯¯¯¯¯
at point O and the zero edge along line segment PQ.
¯¯¯¯¯¯¯¯
(2) Mark a point A at 40∘ . Join OA. OA is the required ray making 40∘ with PQ. D POA is
the supplementary angle of 40∘ .
(3) Draw an arc of convenient radius in the interior of D POA, while taking point O as
centre. Let it both rays of D POA at point B and C.
(4) Draw a line m and mark a point S on it. With the same radius as used before, again
draw an arc while taking point S as centre. Let it cut the line m at point T.
(5) Now, adjust the compasses up to the length of BC. With this radius, draw an arc
while taking T as centre, which will intersect the previously drawn arc at point R.
(6) Join RS. RS is the required ray which makes the same angle with line m, as the
supplementary of 40∘ is 140∘ .
Page : 291 , Block Name : Exercise 14.6
Page 27 of 27 Aglasem Schools
Document Details
| Board / Org | NCERT |
| Exam | Class 6 |
| Type | Solution |
| Pages | 28 |
| Updated | 22 Jul 2026 |