# NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.5

These NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.5 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.5

Question 1.
Draw $$\overline{\mathrm{AB}}$$ of length 7.3 cm and find its axis of symmetry.
Axis of symmetry of line segment $$\overline{\mathrm{AB}}$$ will be the perpendicular bisector of $$\overline{\mathrm{AB}}$$. So, draw the perpendicular bisector of $$\overline{\mathrm{AB}}$$.
Steps of construction:

• Draw a line segment $$\overline{\mathrm{AB}}$$ = 7.3 cm
• Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C and D.
• Join CD. Then CD is the axis of symmetry of the line segment AB.

Question 2.
Draw a line segment of length 9.5 cm and construct its perpendicular bisector.
Steps of construction:

• Draw a line segment $$\overline{\mathrm{AB}}$$ = 9.5 cm
• Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C and D.
• Join CD. Then CD is the 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?
Steps of construction:

• Draw a line segment $$\overline{\mathrm{XY}}$$ = 10.3 cm
• Taking X and Y as centres and radius more than half of AB, draw two arcs which intersect each other at C and D.
• Join CD. Then CD is the required perpendicular bisector of $$\overline{\mathrm{XY}}$$ .

Now:
(a) Take any point P on the bisector drawn. With the help of divider we can check that $$\overline{\mathrm{PX}}$$ = $$\overline{\mathrm{PY}}$$
(b) If M is the mid-point of $$\overline{\mathrm{PX}}$$ and $$\overline{\mathrm{MX}}$$ – 1/2$$\overline{\mathrm{XY}}$$

Question 4.
Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.
Steps of construction:

• Draw a line segment AB = 12.8 cm
• Draw the perpendicular bisector of $$\overline{\mathrm{AB}}$$ which cuts it at C. Thus, C is the midpoint of $$\overline{\mathrm{AB}}$$.
• Draw the perpendicular bisector of $$\overline{\mathrm{AC}}$$ which cuts it at D. Thus D is the midpoint of.
• Again, draw the perpendicular bisector of $$\overline{\mathrm{CB}}$$ which cuts it at E. Thus, E is the mid-point of $$\overline{\mathrm{CB}}$$.
• Now, point C, D and E divide the line segment $$\overline{\mathrm{AB}}$$ in the four equal parts.
• By actual measurement, we find that $$\overline{\mathrm{AD}}=\overline{\mathrm{DC}}=\overline{\mathrm{CE}}=\overline{\mathrm{EB}}$$ = 3.2 cm

Question 5.
With $$\overline{\mathrm{PQ}}$$ of length 6.1 cm as diameter,
draw a circle.
Steps of construction:

• Draw a line segment $$\overline{\mathrm{PQ}}$$ = 6.1 cm.
• Draw the perpendicular bisector of PQ which cuts, it at O. Thus O is the mid-point of $$\overline{\mathrm{PQ}}$$.
• Taking O as centre and OP or OQ as radius draw 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 $$\overline{\mathrm{AB}}$$ and examine if it passes through C.
Steps of construction:

• Draw a circle with centre C and radius 3.4 cm.
• Draw any chord $$\overline{\mathrm{AB}}$$.
• Taking 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.
• Join PQ. Then PQ is the perpendicular bisector of $$\overline{\mathrm{AB}}$$.
• This perpendicular bisector of $$\overline{\mathrm{AB}}$$ passes through the centre C of the circle.

Question 7.
Repeat Q6, if $$\overline{\mathrm{AB}}$$ happens to be a diameter.
Steps of construction:

• Draw a circle with centre C and radius 3.4 cm.
• Draw its diameter $$\overline{\mathrm{AB}}$$.
• Taking A and B as centres and radius more than half of it, draw two arcs which intersect each other at P and Q.
• Join PQ. Then PQ is the perpendicular bisector of $$\overline{\mathrm{AB}}$$ .
• We observe that 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 perpendicular bisectors of these chords.
Where do they meet?
Steps of construction:

• Draw the circle with O and radius 4 cm.
• Draw any two chords $$\overline{\mathrm{AB}}$$ and $$\overline{\mathrm{CD}}$$ in this circle.
• Taking A and B as centres and radius more than half AB, draw two arcs which intersect each other at E and F.
• Join EF. Thus EF is the perpendicular bisector of chord $$\overline{\mathrm{CD}}$$.
• Similarly draw GH the perpendicular bisector of chord $$\overline{\mathrm{CD}}$$.
• These two perpendicular bisectors 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?
• Draw perpendicular bisector of $$\overline{\mathrm{OA}}$$ and OB.
• With the help of divider, we check that $$\overline{\mathrm{PA}}=\mathrm{PB}$$