## MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.3

Question 1.

Draw any line segment \(\overline{P Q}\).Without measuring \(\overline{P Q}\), construct a copy of \(\overline{P Q}\).

Solution:

Steps of construction :

(i) Draw \(\overline{P Q}\)whose length is not known.

(ii) Fix the compasses pointer on P and the pencil end on Q. The opening of the compasses now gives the length of \(\overline{P Q}\)

(iii) Draw any line ‘l’. Choose a point A on ‘l’. Without changing the compasses setting, place the pointer on A.

(iv) Draw an arc that cuts ‘l’ at a point, say B

Now, \(\overline{A B}\) is a copy of \(\overline{P Q}\).

Question 2.

Given some line segment \(\overline{A B}\), whose length you do not know, construct \(\overline{P Q}\) such that the length of \(\overline{P Q}\) is twice that of \(\overline{A B}\)

Solution:

Steps of construction :

(i) Draw \(\overline{A B}\) whose length is not known.

(ii) Fix the compasses pointer on A and the pencil end on The opening of the compasses now gives the length of \(\overline{A B}\).

(iii) Draw any line ‘l’. Choose a point P on ‘l’. Without changing the compasses setting, place the pointer on

(iv) Draw an arc that cuts ‘l’ at a point R.

(v) Now place the pointer on R and without changing the compasses setting, draw another arc that cuts ‘Y at a point Q.

(vi) Thus \(\overline{P Q}\)is the required line segment whose length is twice that of AB.