Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 14 Practical Geometry Ex 14.5 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 6 Maths Chapter 14 Practical Geometry Ex 14.5

Question 1.
Draw (overline{mathrm{AB}}) of length 7.3 cm and find its axis of symmetry.
Note: The perpendicular bisector of a line segment is its axis of symmetry.
Solution:
Steps of construction:
Step I: Draw line segment (overline{mathrm{AB}}) = 7.3 cm.
Step II: With centres A and B and radius more than half of AB, draw two arcs that intersect each other at P and Q.

Step III: Join P and Q.
Thus, PQ is the axis of symmetry of (overline{mathrm{AB}}).

Question 2.
Draw a line segment of length 9.5 cm and construct its perpendicular bisector.
Solution:
Steps of construction:
Step I: Draw a line segment AB = 9.5 cm.
Step II: With A and B as centres and radius more than half of (overline{mathrm{AB}}), draw two arcs on either side of AB which intersects each other at P and Q.

Step III: Join P and Q.
Thus, PQ is the required perpendicular bisector of (overline{mathrm{AB}}).

Question 3.
Draw the perpendicular bisector of (overline{mathrm{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 mid-point of (overline{mathrm{XY}}), what can you say about the lengths MX and XY?
Solution:
Steps of construction:
Step I: Draw a line segment (overline{mathrm{XY}}) = 10.3 cm
Step II: With X and Y as centres and radius more than half of XY, draw two arcs on either side of XY which intersect each other at A and B.
Step III: join A and B.
Thus, AB is ⊥ (overline{mathrm{XY}})

Step IV: Mark a point ‘P’ on AB and join PX and PY.
(a) On measuring (overline{mathrm{PX}}) and (overline{mathrm{PY}}) (using a divider) we get that (overline{mathrm{PX}}) = (overline{mathrm{PY}}) .
(b) The mid-point of XY is M. On measuring,
we have that (overline{mathrm{XM}}) = (overline{mathrm{MY}}) = (frac { 1 }{ 2 }) XY.

Question 4.
Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.
Solution:
Steps of construction:
Step I: Draw a line segment (overline{mathrm{AB}}) = 12.8 cm.

Step II: Draw perpendicular bisector of AB, which meets (overline{mathrm{AB}}) at O. (i.e. O is the mid-point of (overline{mathrm{AB}}))
Step III: Draw perpendicular bisector of (overline{mathrm{AO}}), which meet (overline{mathrm{AB}}) at P. {i.e. P is mid-point of (overline{mathrm{AO}}))
Step IV: Now, draw perpendicular bisector of (overline{mathrm{BO}}), which meets AB at Q. (i.e. Q is the mid-point of OB)
Step V: The line segment is divided into 4 equal parts by the points P, 0 and Q.
Step VI: By actual measurement, we have:
(overline{mathrm{AP}}) = (overline{mathrm{PO}}) = (overline{mathrm{OQ}}) = (overline{mathrm{QB}}) = 3.2 cm

Question 5.
With (overline{mathrm{PQ}}) of length 6.1 cm as diameter, draw a circle.
Solution:
Steps of construction:
Step I: Draw a line segment (overline{mathrm{XY}}) =6.1 cm.
Step II: Draw the perpendicular bisector of PQ which meets (overline{mathrm{XY}}) at O. (i.e. O is the mid-point of PQ).

Step III: With centre O and (overline{mathrm{OP}}) or (overline{mathrm{OQ}}) as radius, draw a circle passing through P and Q.
The circle having (overline{mathrm{XY}}) as the diameter is the required circle.

Question 6.
Draw a circle with centre C and radius 3.4 cm. Draw any chord (overline{mathrm{AB}}).Construct the perpendicular bisector of (overline{mathrm{AB}}) and examine if it passes through C.
Solution:
Steps of construction:
Step I: Mark a point C on a paper.
Step II: With centre ‘C’ and radius 3.4 cm, draw a circle.
Step III: Draw a chord (overline{mathrm{AB}}).
Step IV: Draw perpendicular bisector of (overline{mathrm{AB}}).
We find that l (the perpendicular bisector of (overline{mathrm{AB}})) passes through the centre of the circle.

Question 7.
Repeat question 6, if (overline{mathrm{AB}}) happens to be a diameter.
Solution:
Steps of construction:
Step I: Mark a point ‘C’ on a paper.
Step II: With centre C and radius 3.4 cm, draw a circle.

Step III: Draw a diameter (overline{mathrm{AB}}) of the circle.
Step IV: Draw the perpendicular bisector ‘l’ of (overline{mathrm{AB}}). We find that l passes through C and C is the mid-point of AB.

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:
Steps of construction:
Step I: Mark a point O on a paper.
Step II: With centre O and radius 4 cm, draw a circle.
Step III: Draw two chords (overline{mathrm{AB}}) and (overline{mathrm{CD}}).
Step IV: Draw perpendicular bisector ‘l’ of (overline{mathrm{AB}}).
Step V: Draw perpendicular bisector ‘M’ of (overline{mathrm{CD}}).
Step VI: Produce l and m to meet each other. We find that l and m meet at O, the centre 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 (overline{mathrm{OA}}) and (overline{mathrm{OB}}). Let them meet at P. Is PA = PB?
Solution:
Steps of construction:
Step I: Mark a point O on a paper.
Step II: Draw an angle ∠XOY, having a vertex at O.
Step III: Mark a point A on (overrightarrow{mathrm{OX}}) and another point B on (overrightarrow{mathrm{OY}}), such that (overline{mathrm{OA}}) = (overline{mathrm{OB}}).

Step IV: Draw l, the perpendicular bisector of (overline{mathrm{OB}}) .
Step V: Draw m, the perpendicular bisector of (overline{mathrm{OA}})
Step VI: Mark the intersecting points of l and m as P.
Step VII: Join (overline{mathrm{PA}}) and (overline{mathrm{PB}}), measure them with the help of a divider.
Step VIII: On measuring, we find (overline{mathrm{PA}}) = (overline{mathrm{PB}})