Question

Draw a line, say $AB$ take a point $C$ outside it through $C$, draw a line parallel to $AB$ using ruler and compasses only.

Answer 1

Steps of construction

1. Given a line AB with Point C outside it.
2. Mark point D on the line AB. Join CD
3. With D as center, and any radius, draw an arc intersecting AB at E, and CD at F.
4. With C as center, and same radius as before, draw an arc intersecting CD at G.
5. Open a compass to length EF
6. Now,with G as center, and compass opened the same radius as before, draw an arc intersecting the previous arc at H.
7. Draw a line m passing through C and H.

Thus m is the line parallel to AB, and passing through point C

$\therefore m||AB$