Haryana State Board HBSE 6th Class Maths Solutions Chapter 14 Practical Geometry Ex 14.5 Textbook Exercise Questions and Answers.
Haryana Board 6th Class Maths Solutions Chapter 14 Practical Geometry Exercise
14.5
Question 1.
Draw AB of length 7.3 cm and find its axis of symmetry.
Solution:
Axis of symmetry of line segment \(\overline{\mathrm{AB}}\) will be the perpendicular bisector of \(\overline{\mathrm{AB}}\). So, draw the perpendicular bisector of \(\overline{\mathrm{AB}}\).
(i) Draw a line segment \(\overline{\mathrm{AB}}\) = 7.3 cm.
(ii) With A and B as centres and radius more than half of \(\overline{\mathrm{AB}}\), draw two arcs which intersect each other at C and D.
(iii) Join CD. Then CD is the axis of symmetry of the line segment \(\overline{\mathrm{AB}}\).
Question 2.
Draw a line segment of length 9.5 cm and construct its perpendicular bisector.
Solution:
(i) Draw a line segment \(\overline{\mathrm{AB}}\) = 9.5 cm.
(ii) With A and B as centres and radius more than half of \(\overline{\mathrm{AB}}\), draw two arcs which intersect each other at C and D.
(iii) Join CD. Then CD is the perpendi-cular 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 \(\overline{P X}=\) = \(\overline{P Y}\).
(b) If M is the mid-point of \(\overline{\mathrm{XY}}\). What can you say about the lengths of \(\overline{MX}\) and \(\overline{\mathrm{XY}}\).
Solution:
(i) Draw a line segment \(\overline{\mathrm{XY}}\) = 10.3 cm.
(ii) With X and Y as centres and radius more than half of \(\overline{\mathrm{XY}}\), draw two arcs which cut each other at C and D.
(iii) Join CD. Then, CD is the required perpendicular bisector of \(\overline{\mathrm{XY}}\).
(a) Take any point P on the bisector drawn.
With the help of divider we can check that \(\overline{P X}=\) = \(\overline{P Y}\).
(b) If M is the mid-point of \(\overline{\mathrm{XY}}\), then \(\overline{MX}\) = \(\frac{1}{2}\) \(\overline{\mathrm{XY}}\)
Question 4.
Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal points. Verify by actual measurement.
Solution:
(i) Draw a line segment AB = 12.8 cm.
(ii) Draw the perpendicular bisector of
\(\overline{\mathrm{AB}}\) which cuts it at C. Thus, C is the midpoint of \(\overline{\mathrm{AB}}\).
(iii) Draw the perpendicular bisector of \(\overline{\mathrm{AC}}\) which cuts it at D. Thus, D is the mid-point of \(\overline{\mathrm{AC}}\).
(iv) Again, draw the perpendicular bisector of \(\overline{\mathrm{CB}}\) which cuts it at E. Thus, E is the mid-point of \(\overline{\mathrm{CB}}\).
(v) Now, points D, C and E divide the line segment \(\overline{\mathrm{AB}}\) into four equal parts.
(vi) By actual measurement, we find that \(\overline{\mathrm{AD}}=\overline{\mathrm{DC}}=\overline{\mathrm{CE}}=\overline{\mathrm{EB}}=3.2 \mathrm{~cm}\)
Question 5.
With \(\overline{\mathrm{PQ}}\) of length 6.1 cm as diameter draw a circle.
Solution:
(i) Draw a line segment \(\overline{\mathrm{PQ}}\) =6.1 cm.
(ii) Draw the per¬pendicular bisector of PQ which cuts it at O. Thus, O is the mid-point of \(\overline{\mathrm{PQ}}\).
(iii) With 0 as centre and OP or OQ as radius, draws a circle where diameter is the line segment \(\overline{\mathrm{PQ}}\).
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:
(i) Draw a circle Fig. with centre C and radius 3.4 cm.
(ii) Draw any chord \(\overline{\mathrm{AB}}\).
(iii) With A and B as centres and radius more than half of \(\overline{\mathrm{AB}}\), draw two arcs which cut each other at P and Q.
(iv) Join \(\overline{\mathrm{PQ}}\). Then, PQ is the perpendicular bisector of \(\overline{\mathrm{AB}}\).
(v) Clearly, this perpendicular bisector of \(\overline{\mathrm{AB}}\) passes through the centre C of the circle.
Question 7.
Repeat Question 6, if AB happens to be a diameter.
Solution:
(i) Draw a circle with centre C and radius 3.4 cm.
(ii) Draw its diameter \(\overline{\mathrm{AB}}\).
(iii) With A and B as centres and radius more than half of \(\overline{\mathrm{AB}}\), draw two arcs which cut each other at P arid Q.
(iv) Join \(\overline{\mathrm{PQ}}\). Then PQ is the perpendi¬cular bisector of \(\overline{\mathrm{AB}}\).
(v) Clearly, this perpendicular bisector of \(\overline{\mathrm{AB}}\) passes through the centre C of the circle.
Question 8.
Draw a circle of radius 4 cm. Draw any two of its chords. Construct the per-pendicular bisectors of these chords. Where do they meet ?
Solution:
(i) Draw a circle with centre 0 and radius 4 cm.
(ii) Draw any two chords \(\overline{\mathrm{AB}}\) and \(\overline{\mathrm{CD}}\) of this circle.
(iii) With A and B as centres and radius more that half of \(\overline{\mathrm{AB}}\), draw two arcs which cut each other at E and F.
(iv) Join EF. Thus, EF is the perpendi-cular bisector of chord \(\overline{\mathrm{AB}}\).
(v) Similarly, draw GH the perpendicular bisector of chord \(\overline{\mathrm{CD}}\) .
(vi) These two perpendicular bisectors meet at 0, 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 bisector of \(\overrightarrow{\mathrm{OA}}\) and \(\overline{\mathrm{OB}}\). Let them meet at P. Is \(\overline{\mathrm{PA}}=\overline{\mathrm{PB}}\) ?
Solution:
(i) Draw any angle with vertex 0.
(ii) Take a point A on one of its arms and B on another such that \(\overline{\mathrm{OA}}=\overline{\mathrm{OB}}\).
(iii) Draw perpen¬dicular bisectors of \(\overline{\mathrm{OA}}\) and \(\overline{\mathrm{OB}}\).
(iv) Let them meet at P. Join PA and PB.
(v) With the help of divider we can check that \(\overline{\mathrm{PA}}=\overline{\mathrm{PB}}\).
