Question

Draw a line PQ Take a point M outside it through M draw a line parallel to PQ using compasses and reder

Answer 1

To draw a parallel line to PQ through M follow the below procedure:

1. Draw a line PQ of any length.
2. Now mark a point M outside the line PQ.
3. Now make a line joining M and intersecting PQ.
4. Now take any length in the compass and point the compass at the intersection of line through M and line PQ and mark an arc starting from PQ and the line through M.
5. Similarly , with the same length in the compass , place the compass at M and mark a similar arc as the above arc.
6. Now place the compass on the intersection of line through M and measure the length where the arc intersects the line PQ.
7. Now with the same length place the compass on the intersection of arc drawn from M and the line and mark an arc that intersects the arc as shown in figure.
8. Now join the points M and the intersection of arc to obtain the parallel line through M.

Answer 2

Answer

Given a line PQ with point A outside it.

2. Mark point B on the lie PQ join AB.

3. Taking B as centre, and any radius, draw an arc intersecting PQ at E, and AB at D.

4. With A as centre, and same radius before, draw an arc intersecting AB at F.

5. Open compass to length DE.

6. Now, with F as centre, and compass opened the same radius as before, draw an arc intersecting the previous arc at H.

7. Draw a line m passing through A and H.

Thus m is parallel to PQ, and passing through point A.

∴m∣∣PQ.