# NCERT Solutions For Class 6 Maths Practical Geometry Exercise 14.5

## 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

Ex 14.5 Class 6 Maths Question 1.
Draw AB of length 7.3 cm and find its axis of symmetry.
Solution:
Step I: Draw $\overline { AB }$= 7.3 cm

Step II: Taking A and B as centre and radius more than half of $\overline { AB }$, draw two arcs which intersect each other at C and D.
Step III: Join C and D to intersect $\overline { AB }$at E. Thus, CD is the perpendicular bisector or axis of symmetry of $\overline { AB }$.

Ex 14.5 Class 6 Maths Question 2.
Draw a line segment of length 9.5 cm and construct its perpendicular bisector.
Solution:
Step I: Draw a line segment $\overline { PQ }$=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 $\overline { PQ }$at T.
Thus, RS is the perpendicular bisector of PQ.

Ex 14.5 Class 6 Maths Question 3.
Draw the perpendicular bisector of $\overline { XY }$whose length is 10.3 cm.
(a) Take any point P on the bisector drawn. Examine whether PX = PY.
(b) If M is the midpoint of $\overline { XY }$. What can you say about the length of MX and MY?
Solution:
Step I: Draw a line segment $\overline { XY }$= 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 $\overline { XY }$at M.
Step IV: Take a point P on $\overline { UV }$.
(a) On measuring, PX = PY = 5.6 cm.
(b) On measuring, $\overline { MX }$= $\overline { MY }$= $\frac { 1 }{ 2 }$XY = 5.15 cm.

Ex 14.5 Class 6 Maths 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 $\overline { AB }$= 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 $\overline { AB }$at C which is the midpoint of $\overline { AB }$.
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 $\overline { AC }$at H which is the midpoint of $\overline { AC }$.
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 $\overline { CB }$at L which is the midpoint of $\overline { CB }$.
Thus, on measuring, we find
$\overline { AH }$= $\overline { HC }$= $\overline { CL }$= $\overline { LB }$= 3.2 cm.

Ex 14.5 Class 6 Maths Question 5.
With $\overline { PQ }$of length 6.1 cm as diameter, draw a circle.
Solution:
Step I: Draw $\overline { PQ }$= 6.1 cm
Step II: Draw a perpendicular bisector of $\overline { PQ }$which meets $\overline { PQ }$at R i.e. R is the midpoint of $\overline { PQ }$.

Step III : With centre R and radius equal to $\overline { RP }$, draw a circle passing through P and Q.
Thus, the circle with diameter $\overline { PQ }$= 6.1 cm is the required circle.

Ex 14.5 Class 6 Maths Question 6.
Draw a circle with centre C and radius 3.4 cm. Draw any chord $\overline { AB }$. Construct the perpendicular bisector of $\overline { AB }$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 $\overline { AB }$.
Step III : Draw the perpendicular bisector of $\overline { AB }$which passes through the centre C.

Ex 14.5 Class 6 Maths Question 7.
Repeat Question number 6, if $\overline { AB }$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 $\overline { AB }$.

Ex 14.5 Class 6 Maths 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 $\overline { AB }$and $\overline { CD }$of the circle.
Step III : Draw the perpendicular bisectors of $\overline { AB }$and $\overline { CD }$i.e. I and m.
Step IV : On producing the two perpendicular bisectors meet each other at the centre O of the circle.

Ex 14.5 Class 6 Maths 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 $\overline { OA }$and $\overline { OB }$. 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 $\overline { PA }$and $\overline { PB }$. Yes, $\overline { PA }$= $\overline { PB }$.

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