NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.5

*According to the latest update on the CBSE Syllabus 2023-24, this chapter has been removed.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.5 have been created by the faculty at BYJU’S to help the students prepare for their exams efficiently. The perpendicular bisector of a line segment and the steps to be followed in their construction using a compass and ruler are explained in a simple way under Exercise 14.5. The steps in the construction of a line segment are discussed in an interactive manner in these NCERT Solutions, with the aim of making it easily understandable for the students.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.5

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Access NCERT Solutions for Class 6 Maths 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:

The 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 - 3 of 7.3 cm.

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

(2) Take A as the centre and draw a circle by using compasses. The radius of the 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 the 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:

The 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 the centre and draw a circle by using compasses. The radius of the 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 midpoint 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 the centre and draw a circle by using compasses. The radius of the 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 the centre, draw another circle using compasses with the same radius as before. Let it cut at the 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 the same,

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 28 being the axis of symmetry, any point lying on NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 29will be at the same distance from 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, the 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 the 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 the 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 a 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 the centre and with the 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 intersect 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 - 48NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 49NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 - 50NCERT 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 3.2 cm.

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

Solution:

(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 the 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 the same radius and Q as the 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 a 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 compass up to 3.4 cm, and by putting the pointer of the compass at point C, turn the compass slowly to draw the circle. This is the required circle with 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 compass up to 3.4 cm, and by putting the pointer of the compass at point C, turn the compass slowly to draw the circle. This is the required circle with 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 a 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 the 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 O on the sheet. Now adjust the compass up to 4 cm, and by placing the pointer of the compass at point O, turn the compass slowly to draw the circle. This is the required circle with 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 a 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 intersect each other at points E and F. Join EF, which is the 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 a 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 intersect each other at points G, H. Join GH, which is the 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 point O, which is the centre of the circle.

9. Draw any angle with vertex O. Take 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 the centre and with a convenient radius, draw arcs on both rays of this angle. Let these points be 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 a radius of more than half of OA, draw arcs on both sides of OA. Let these intersect 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 the 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 - 95, intersect 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


Also, explore –

NCERT Solutions for Class 6 Maths Chapter 14

NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6

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