Constructing the perpendicular from a point to a line

           When two lines intersect to form right angles then such lines are known as Perpendicular to each other. Perpendicular lines are Co-Planar (i.e., They lie in same plane) and intersect at right angle (90°).

Method 1: Constructing a perpendicular to a line through a point on it

1) Assume given line as AB and a point P is present near middle of the line on it,

2) Taking P as a center and any suitable radius on compass, draw an arc cutting line segment AB at two distinct points (C, D) as shown below

3) Taking C as centre and a suitable radius (more than CP or DP distance) draw an arc above the line segment, with D as centre and the same radius as previous, draw an arc cutting previously drawn arc,

4) Mark the intersecting point as E.

5) Join the points E and P as shown, and the line segment EP is the required perpendicular to line AB through point P.

Note: This method we follow when we don't have Protractor with us.