Introduction :
Perpendicular means a line whcih makes an angle of 90 degrees with the given line.Here we will learn the steps to construct a perpendicular line to a given
line.
Learning the steps to construct a perpendicular to a line :

Step1: Draw the given line segment AB of given length.

Step 2: With centre A and radius more than AB , draw arcs , one on each side of AB .

Step 3: With centre B and same radius as before, draw arcs , one on each side of AB ., cutting the previous arcs at E and F respectively.

Step 4: Join the EF intersecting at M. Then line EM is perpendicular to AB.
Learning examples to construct a perpendicular to a line
1) Draw a line segment of length 6.6 cm. Construct perpendicular line for the given line segment.
Solution: Steps of construction:

Step 1: Draw a line segment AB = 6.6 cm by using a ruler.

Step 2: With A as centre and radius more than half of AB, draw arcs, one on each side of AB.

Step 3: With B as centre and the same radius as in Step 2, draw arcs cutting the arcs drawn in Step 2 at E and F points respectively.

Step 4: Draw a line segment joining E and F as end points. Thus EF is perpendicular to AB.
Learning construct a perpendicular to a circle
Learning steps to construct a perpendicular to a circle
A line perpendicular to a circle is called a tangent.
Construct a tangent to a circle at a given point

Step 1 : Take a point O on the plane of the paper and draw a circle of given radius.

Step 2: Take a point P on the circle

Step 4 : Construct <OPT = 90 ^{0} .

Step 5 : Produce TP to T' to get the required tangent T'PT