Answer:

To construct a line parallel to the other line from an external point we require a ruler and a compass and the following steps are followed:

Given: A line segment AB and a point P that lies out of the line segment AB

To construct a line that is parallel to line AB that passes through point P.

Step 2: With X as center and any suitable radius draw an arc cutting the line segment PX at point M and AB at point N respectively.

Constructing of Parallel Lines 3

Step 3: With P as center and radius as used in the previous step draw an arc EF cutting the line segment PX at point Q as shown.

Constructing of Parallel Lines 4

Step 4: With Q as center and same radius as before, draw an arc cutting the arc EF at R as shown below.

Constructing of Parallel Lines 5

Step 5: Join R and P to draw a line segment CD as shown.

Constructing of Parallel Lines 6

The line segment CD is the required line parallel to the line segment AB and passes through the point P.

Step-by-step explanation: