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

Exercise 14.5

1. Draw AB of length \[7.3cm\]and find its axis of symmetry. 

Ans:  Axis of symmetry of line segment AB will be the perpendicular bisector of AB. So, draw the perpendicular bisector of AB. 

Steps of Construction:

1. Draw a line segment AB \[ = 7.3cm\]

2. Taking A and B as centres and radius more than half of AB, one circle and arch which intersect each other at C and D. 

3. Join the line CD. 

4. The axis of symmetry of the line segment AB. 

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

Ans: Steps of Construction:

1. Draw a line segment PQ\[ = 9.5cm\]

2. Taking P and Q as centres and the radius is more than half of PQ, draw one circle and arch which intersect each other at R and S. 

3. Join RS. 

4. RS is the perpendicular bisector of PQ. 

3. Draw the perpendicular bisector of XY whose length is \[10.3cm\].

1. Take any point P on the bisector drawn. Examine whether PX = PY. 

2. If M is the midpoint of XY , what can you say about the lengths MX and XY? 

Ans: Steps of Construction:

1. Draw a line segment XY \[ = 10.3cm\]

2. Taking X and Y as centres and radius more than half of XY, draw one circle and arc which intersect each other at A and B. 

3. Join AB. 

4. AB is the required perpendicular bisector of XY 

Then take any point P on the bisector. We can  conclude PX = PY

If M is the midpoint of XY, then \[{\text{MX}} = \left( {\frac{1}{2}} \right){\text{XY}}\]

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

Ans: Steps of Construction:

1. Draw a line segment XY\[ = 12.8cm\]

2. Draw the perpendicular bisector of XYwhich cuts it at M. 

3. M is the midpoint of XY. 

4. Draw the perpendicular bisector of XM which cuts it at T. 

5. T is the mid-point of XM. 

6. Draw the perpendicular bisector of MY which cuts it at U. 

7. U is the mid- point of MY. 

8. Now, point T,M and U divide the line segment XY in the four equal parts. 

9. By actual measurement, we find that 

\[{\text{XT = TM = MU = UY = }}3.2cm\]

5. With PQ of length \[6.1cm\]as diameter, draw a circle. 

Ans: Steps of Construction:

1. Draw a line segment PQ \[ = 6.1cm\]. 

2. Draw the perpendicular bisector of PQ which intersects at point O. 

3. T is the midpoint of PQ. 

4. Taking O as centre and TP or TQ as radius draw a circle where diameter is the line segment PQ. 

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

Ans: Steps of construction:

1. Draw a circle with centre C and radius \[3.4cm\]. 

2. Draw any chord AB. 

3. Taking A and B as centers and radius more than half of AB, draw two arcs which cut each other at E and D. 

4. Join ED. Then ED is the perpendicular bisector of AB. 

The perpendicular bisector of AB passes through the C.

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

Ans: Steps of Construction:

1. Draw a circle with centre C and of radius \[3.4cm\]. 

2. Draw its diameter AB. 

3. Taking A and B as centers and radius more than half of it. 

4. Draw two arcs which intersect each other at point E and point D. 

5. Join ED. 

6. Then ED is the perpendicular bisector of AB. 

7. We observe that this perpendicular bisector of AB passes through the centre C of the circle.

8. Draw a circle of radius \[4cm\]. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet? 

Ans: Steps of construction:

1. Draw a circle with center O and radius \[4cm\]. 

2. Draw any two chords AB and CD in this circle. 

3. Taking A and B as centers and radius more than half of AB, draw two arcs such that they intersect each other at E and F. 

4. Join EF. 

5. EF is the perpendicular bisector of the chord CD. 

6. Draw GH the perpendicular bisector of the chord CD .

7. The perpendicular bisectors EF and GH meet at point O.

9. Draw any angle with vertex O. Take a point A on one of its arms and B on another such that \[{\text{OA = OB}}\]. Draw the perpendicular bisectors of OA and OB. Let them meet at P. Is \[{\text{PA = PB}}\]?

Ans: Steps of Construction:

1. Draw any angle with vertex O. 

2. Take a point A on one of its arms and B on another such that \[{\text{OA = OB}}\] .

3. Draw perpendicular bisectors of OA and OB. 

4. Let them meet at P. Join PA and PB. 

5. Check that \[{\text{PA = PB}}\].

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

Opting for the NCERT solutions for Ex 14.5 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 14.5 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 6 students who are thorough with all the concepts from the Subject Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 6 Maths Chapter 14 Exercise 14.5 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 6 Maths Chapter 14 Exercise 14.5, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 

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