NCERT Solutions For Class 6 Maths Ex 14.5

NCERT Solutions For Class 6 Maths Ex 14.5 PDF Free Download

Perpendicular bisector of a line segment and steps to be followed in their construction using compass and ruler are explained in a simple way under exercise 14.5. The steps in construction of line segment are discussed in an interactive manner with the aim of making it easily understandable for the students. To gain expertise in these concepts and score well in the exam, students can refer NCERT Solutions Class 6 Maths Chapter 14 Practical Geometry Exercise 14.5 PDF, which are provided below.

NCERT Solutions for Class 6 Chapter 14: Practical Geometry Exercise 14.5 Download PDF

 

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

 

Access NCERT Solutions for Class 6 Chapter 14: Practical Geometry Exercise 14.5

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


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