Construction Of Parallel Lines

Have you ever observed the railway tracks or the opposite edges of a door? One of the interesting fact about these is that they are examples of parallel lines. Now the question arises what exactly are parallel lines? The lines which do not have a common meeting point in the same plane, however far they are extended are known as parallel lines. The following figure represents parallel lines:

Parallel Lines

Two lines are said to be parallel in a plane if they do not intersect if extended till infinite in both the direction. The distance between the two lines is similar throughout the whole length. The symbol to denote the parallel lines is ||. Suppose the two lines ‘a’ and ‘b’ are parallel to each other, we can express their parallel nature by a||b and read as ‘a is parallel to b’.

Construction of Parallel Lines:

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 perpendicular to line AB that passes through point P.

Construction Steps:

  • Step 1: Choose any point X on the line segment AB and join it to point P as shown.

Parallel Lines

  • 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.

Parallel Lines

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

Parallel Lines

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

Parallel Lines

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

Parallel Lines

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

To verify whether the line segment that is constructed is parallel to line segment AB, connect the points E,Q and M, N as described below:

Parallel Lines

In the triangle EPQ and XMN,

Parallel Lines

To learn more about construction of parallel lines and slope of line, download BYJU’s-The Learning App and improve your skills.

Practise This Question

Assume line m and line n are parallel lines cut by the transversal line l.  Find the value of x.