NCERT Solutions Class 6 Maths Chapter 14 Practical Geometry Ex 14.5

NCERT Solutions Class 6 Maths
Chapter – 14 (Practical Geometry)

The NCERT Solutions in English Language for Class 6 Mathematics Chapter – 14 Practical Geometry Exercise 14.5 has been provided here to help the students in solving the questions from this exercise.

Chapter 14: Practical Geometry

Exercise – 14.5

1. Draw $\mathbf{\overline{AB}}$ of length 7.3 cm and find its axis of symmetry.

Solutions:

Following steps are followed to construct $\overline{AB}$ of length 7.3 cm and to find its axis of symmetry.
$NCERT Class 6 Math Solution$
Step 1: Draw $\overline{AB}$ = 7.3 cm.
Step 2: 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 3: Join C and D to intersect $\overline{AB}$ at E. Thus, CD is the perpendicular bisector or axis of symmetry of $\overline{AB}$ .

2. Draw a line segment of length 9.5 cm and construct its perpendicular bisector.

Solutions:

Following steps are observed to construct a line segment of length 9.5 cm and to construct its perpendicular bisector.

Step 1: Draw a line segment $\overline{PQ}$ =9.5 cm.
Step 2: With centres P and Q and radius more than half of PQ, draw two arcs which meet each other at R and S.
Step 3: Join R and S to meet $\overline{PQ}$ at T.
Thus, RS is the perpendicular bisector of $\overline{PQ}$ .

3. Draw the perpendicular bisector of $\mathbf{\overline{XY}}$ whose length is 10.3 cm.
(a) Take any point P on the bisector drawn. Examine whether PX = PY.
(b) If M is the mid point of $\overline{XY}$ , what can you say about the lengths MX and XY?

Solutions:
$NCERT Class 6 Math Solution$
Step 1: Draw a line segment $\overline{XY}$ = 10.3 cm.
Step 2: With centre X and Y and radius more than half of XY, draw two arcs which meet each other at U and V.
Step 3: Join U and V which meets $\overline{XY}$ at M.
Step 4: 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.

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

Solutions:
$NCERT Class 6 Math Solution$
Step 1: Draw a line segment $\overline{AB}$ = 12.8 cm
Step 2: With centre A and B and radius more than half of AB, draw two arcs which meet each other at D and E.
Step 3: Join D and E which meets $\overline{AB}$ at C which is the midpoint of $\overline{AB}$ .
Step 4: With centre A and C and radius more than half of AC, draw two arcs which meet each other at F and G.
Step 5: Join F and G which meets $\overline{AC}$ at H which is the midpoint of $\overline{AC}$ .
Step 6: With centre C and B and radius more than half of CB, draw two arcs which meet each other at J and K.
Step 7: 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.

5. With $\mathbf{\overline{PQ}}$ of length 6.1 cm as diameter, draw a circle.

Solutions:
$NCERT Class 6 Math Solution$
Step 1: $\overline{PQ}$ = 6.1 cm
Step 2: Draw a perpendicular bisector of $\overline{PQ}$ which meets $\overline{PQ}$ at R i.e. R is the midpoint of $\overline{PQ}$ .
Step 3: 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.

6. Draw a circle with centre C and radius 3.4 cm. Draw any chord $\mathbf{\overline{AB}}$ . Construct the perpendicular bisector of $\mathbf{\overline{AB}}$ and examine if it passes through C.

Solutions:
$NCERT Class 6 Math Solution$
Step 1: Draw a circle with centre C and radius 3.4 cm.
Step 2: Draw any chord $\overline{AB}$ .
Step 3: Draw the perpendicular bisector of $\overline{AB}$ which passes through the centre C.

7. Repeat Question 6, if $\mathbf{\overline{AB}}$ happens to be a diameter.

Solutions:
$NCERT Class 6 Math Solution$
Step 1: Draw a circle with centre C and radius 3.4 cm.
Step 2: Draw a diameter AB of the circle.
Step 3: Draw a perpendicular bisector of AB which passes through the centre C and on measuring, we find that C is the midpoint of $\overline{AB}$ .

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?

Solutions:
$NCERT Class 6 Math Solution$
Step 1: Draw a circle with centre 0 and radius 4 cm.
Step 2: Draw any two chords $\overline{AB}$ and $\overline{CD}$ of the circle.
Step 3: Draw the perpendicular bisectors of $\overline{AB}$ and $\overline{CD}$ i.e. I and m.
Step 4: On producing the two perpendicular bisectors meet each other at the centre O of the circle.

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 $\mathbf{\overline{OA}}$ and $\mathbf{\overline{OB}}$ . Let them meet at P. Is PA = PB?

Solutions:
$NCERT Class 6 Math Solution$
Step 1: Draw an angle XOY with O as its vertex.
Step 2: Take any point A on OY and B on OX, such that OA + OB.
Step 3: Draw the perpendicular bisectors of OA and OB which meet each other at a point P.
Step 4: Measure the lengths of $\overline{PA}$ and $\overline{PB}$ . Yes, $\overline{PA}$ = $\overline{PB}$ .

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NCERT Solutions Class 6 Maths Chapter 14 Practical Geometry Ex 14.5