# NCERT Solutions For Class 6 Maths Chapter 14 Practical Geometry Exercise 14.5

NCERT Solutions For Class 6 Maths Chapter 14 Practical Geometry Exercise 14.5 has been created by the faculty at BYJUâ€™S to help the students prepare for their exams efficiently. The 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 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 Download PDF

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

1. Draw of length 7.3 cm and find its axis of symmetry.

Solutions:

Following steps are followed to constructÂ  of length 7.3 cm and to find its axis of symmetry

(1) Draw a line segmentÂ Â of 7.3 cm

(2) Take A as centre and draw a circle by using compasses. The radius of circle should be more than half the length of
.

(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

(4) Join CD. NowÂ is the axis of symmetry

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 segmentÂ of 9.5 cm

(2) Take point P as centre and draw a circle by using compasses. The radius of circle should be more than half the length ofÂ

(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.

(4) Join RS. Now,Â is the axis of symmetry i.e the perpendicular bisector of the lineÂ

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3. Draw the perpendicular bisector of 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 , what can you say about the lengths MX and XY?

Solutions:

(1) Draw a line segment Â of 10.3 cm

(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

(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

(4) Join AB. HereÂ is the axis of symmetry

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(a) Take any point P onÂ . We may observe that the measure of lengths of PX and PY are same

Â being the axis of symmetry, any point lying onÂ will be at same distance from the both ends of

(b) M is the midpoint of . Perpendicular bisectorÂ will be passing through point M. Hence length of
is double ofÂ or 2MX = XY.

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 Â of 12.8 cm

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

(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 Â at point M

(4) By taking X and Y as centres, draw two circles with radius more than half ofÂ

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

(6) Join PQ, and RS. These are intersecting Â at points T and U.

(7) The 4 equal parts of Â areÂ =Â =Â =Â

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

5. With of length 6.1 cm as diameter, draw a circle.

Solutions:

(1) Draw a line segment Â of 6.1 cm

(2) Take point P as centre and radius more than half of , draw a circle

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

(4) Join RS which intersects Â at T.

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

6. Draw a circle with centre C and radius 3.4 cm. Draw any chord . Construct the perpendicular bisector of 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.

(3) Mark any chord Â in the circle

(4) Now, taking A and B as centres, draw arcs on both sides of . Let these intersect each other at points D and E.

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

IfÂ is extended, it will pass through point C.

7. Repeat Question 6, if 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

(3) Now mark any diameter Â in the circle.

(4) Now taking A and B as centres, draw arcs on both sides of Â with radius more than . Let these intersect each other at points D and E.

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

Now, we may observe thatÂ is 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 compasses up to 4 cm and by placing the pointer of compasses at point O, turn the compasses slowly to draw the circle. This is the required circle of 4 cm radius

(2) Take any two chords Â andÂ in the circle

(3) By taking A and B as centres and radius more than half of , 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.

(4) Again take C and D as centres and radius more than half ofÂ , 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

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 and . Let them meet at P. Is PA = PB?

Solutions:

(1) Draw any angle with vertex as O.

(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

(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

(4) Similarly we may findÂ which is perpendicular bisector of . These perpendicular bisectorsÂ andÂ intersects each other at point P. Now measure PA and PB. They are equal in length.