Class 6 - Mathematics : Practical Geometry
Exercise : 14.3
Top Block 1
Question: 1.Draw any line segment PQ. Without measuring PQ, construct a copy of PQ.
Answer :
Steps of construction:
(i) Given PQ whose length is not known.
(ii) Fix the compasses pointer on P and the pencil end on Q. The opening of the instrument now gives the length of PQ.
(iii) Draw any line ′l′. Choose a point A on ′l′. Without changing the compasses setting, place the pointer on A.
Draw an arc that cuts ′l′ at a point, say B. Now AB is a copy of PQ.
(ii) Fix the compasses pointer on P and the pencil end on Q. The opening of the instrument now gives the length of PQ.
(iii) Draw any line ′l′. Choose a point A on ′l′. Without changing the compasses setting, place the pointer on A.
Draw an arc that cuts ′l′ at a point, say B. Now AB is a copy of PQ.
Question: 2.Given some line segment AB, whose length you do not know, construct PQ such that the length of PQ is twice that of AB.
Answer :
Steps of construction:
Mddle block 1
(i) Given AB whose length is not known.
(ii) Fix the compasses pointer on A and the pencil end on B. The opening of the instrument now gives the length of AB.
(iii) Draw any line ′l′. Choose a point P on ′l′. Without changing the compasses setting, place the pointer on Q.
(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 ′l′ at a point Q.
Thus PQ is the required line segment whose length is twice that of AB.
(ii) Fix the compasses pointer on A and the pencil end on B. The opening of the instrument now gives the length of AB.
(iii) Draw any line ′l′. Choose a point P on ′l′. Without changing the compasses setting, place the pointer on Q.
(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 ′l′ at a point Q.
Thus PQ is the required line segment whose length is twice that of AB.