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

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

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

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.5 are the part of NCERT Solutions for Class 6 Maths. Here you can find the NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.5.

### Ex 14.5 Class 6 Maths Question 1.

Draw AB of length 7.3 cm and find its axis of symmetry.

Solution:

The perpendicular bisector of a line segment is its axis of symmetry.
Step 1: Draw a line segment AB = 7.3 cm.

Step 2: Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C and D.
Step 3: Join C and D to intersect AB at E.

Thus, CD is the axis of symmetry of 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 1: Draw a line segment PQ = 9.5 cm.

Step 2: With centres P and Q and radius more than half of PQ, draw two arcs which intersect each other at R and S.
Step 3: Join R and S to meet PQ at T.
Thus, RS is the perpendicular bisector of PQ.

### Ex 14.5 Class 6 Maths Question 3.

Draw the perpendicular bisector of 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 XY. What can you say about the length of MX and MY?

Solution:
Step 1: Draw a line segment XY = 10.3 cm.

Step 2: With centres X and Y and radius more than half of XY, draw two arcs which intersect each other at U and V.
Step 3: Join U and V which intersects XY at M.
Step 4: Take a point P on UV.
(a) On measuring, PX = PY = 5.6 cm.
(b) On measuring, MX = MY = ½ 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 1: Draw a line segment AB = 12.8 cm

Step 2: With centres A and B and radius more than half of AB, draw two arcs which intersect each other at D and E.
Step 3: Join D and E which intersectAB at C which is the midpoint of AB.
Step 4: With centres A and C and radius more than half of AC, draw two arcs which intersect each other at F and G.
Step 5: Join F and G which intersectAC at H which is the midpoint of AC.
Step 6: With centres C and B and radius more than half of CB, draw two arcs which intersect each other at J and K.
Step 7: Join J and K which intersectCB at L which is the midpoint of CB.
Thus, on measuring, we find
AH = HC = CL = LB = 3.2 cm.

### Ex 14.5 Class 6 Maths Question 5.

With PQ of length 6.1 cm as diameter, draw a circle.

Solution:
Step 1: Draw a line segment PQ = 6.1 cm.
Step 2: Draw a perpendicular bisector of PQ which intersectPQ at R, i.e., R is the midpoint of PQ.

Step 3: With centre R and radius equal to RP, draw a circle passing through P and Q.
Thus, the circle with diameter PQ = 6.1 cm is drawn.

### Ex 14.5 Class 6 Maths Question 6.

Draw a circle with centre C and radius 3.4 cm. Draw any chord AB. Construct the perpendicular bisector of AB and examine if it passes through C.

Solution:
Step 1: Draw a circle with centre C and radius 3.4 cm.
Step 2: Draw a chord AB of the circle.
Step 3: Draw the perpendicular bisector of AB which passes through the centre C.

### Ex 14.5 Class 6 Maths Question 7.

Repeat Question 6, if AB happens to be a diameter.

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 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 1: Draw a circle with centre O and radius 4 cm.

Step 2: Draw any two chords AB and CD of the circle.
Step 3: Draw the perpendicular bisectors of AB and CD, i.e., I and m.
Step 4: On producing, the two perpendicular bisectors intersect 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 OA and OB. Let them meet at P. Is PA = PB?

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 intersect each other at a point P.
Step 4: Measure the lengths of PA and PB. Yes, PA = PB.

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