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

**NCERT Solutions For Class 6 Maths Chapter 14 Practical Geometry Ex 14.5**

**Exercise 14.5**

Question 1.

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

Solution:

Step I: Draw = 7.3 cm

Step II: Taking A and B as centre and radius more than half of , draw two arcs which intersect each other at C and D.

Step III: Join C and D to intersect at E. Thus, CD is the perpendicular bisector or axis of symmetry of .

Question 2.

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

Solution:

Step I: Draw a line segment =9.5 cm

Step II: With centres P and Q and radius more than half of PQ, draw two arcs which meet each other at R and S.

Step III: Join R and S to meet at T.

Thus, RS is the perpendicular bisector of PQ.

Question 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 midpoint of . What can you say about the length of MX and MY?

Solution:

Step I: Draw a line segment = 10.3 cm.

Step II : With centre X and Y and radius more than half of XY, draw two arcs which meet each other at U and V.

Step III: Join U and V which meets at M.

Step IV: Take a point P on .

(a) On measuring, PX = PY = 5.6 cm.

(b) On measuring, = = XY = 5.15 cm.

Question 4.

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

Solution:

Step I: Draw a line segment = 12.8 cm

Step II : With centre A and B and radius more than half of AB, draw two arcs which meet each other at D and E.

Step III : Join D and E which meets at C which is the midpoint of .

Step IV : With centre A and C and radius more than half of AC, draw two arcs which meet each other at F and G.

Step V: Join F and G which meets at H which is the midpoint of .

Step VI : With centre C and B and radius more than half of CB, draw two arcs which meet each other at J and K.

Step VII : Join J and K which meets at L which is the midpoint of .

Thus, on measuring, we find

= = = = 3.2 cm.

Question 5.

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

Solution:

Step I: Draw = 6.1 cm

Step II: Draw a perpendicular bisector of which meets at R i.e. R is the midpoint of .

Step III : With centre R and radius equal to , draw a circle passing through P and Q.

Thus, the circle with diameter = 6.1 cm is the required circle.

Question 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.

Solution:

Step I: Draw a circle with centre C and radius 3.4 cm.

Step II: Draw any chord .

Step III : Draw the perpendicular bisector of which passes through the centre C.

Question 7.

Repeat Question number 6, if happens to be a diameter.

Solution:

Step I: Draw a circle with centre C and radius 3.4 cm.

Step II : Draw a diameter AB of the circle.

Step III : Draw a perpendicular bisector of AB which passes through the centre C and on measuring, we find that C is the midpoint of .

Question 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?

Solution:

Step I: Draw a circle with centre 0 and radius 4 cm.

Step II: Draw any two chords and of the circle.

Step III : Draw the perpendicular bisectors of and i.e. I and m.

Step IV : On producing the two perpendicular bisectors meet each other at the centre O of the circle.

Question 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?

Solution:

Step I: Draw an angle XOY with O as its vertex.

Step II : Take any point A on OY and B on OX, such that OA + OB.

Step III : Draw the perpendicular bisectors of OA and OB which meet each other at a point P.

Step IV : Measure the lengths of and . Yes, = .

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