# Learning Construct a Perpendicular

## 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 3: Join OP

• Step 4 : Construct <OPT = 90 0 .

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