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, $\overline { PA }$ = $\overline { PB }$ .