Construction of Perpendicular Lines:

When two lines intersect to form right angles then such lines are known as perpendicular to each other. Perpendicular lines lie in the same plane i.e. they are co-planar and intersect at right angles. Thus it implies that if you have two lines which are perpendicular to each other, then these lines will be at right angles and vice versa. With the help of ruler and compass we can easily construct a line perpendicular to another line and passing through a point given on that line.

Constructing a perpendicular to a line through a point on it

Given: A line segment AB with a point P on it.

To construct: A line perpendicular to line AB passing through point P.

Steps for Construction:

Step 1: With P as center and any suitable radius, draw an arc cutting line segment AB at two distinct points as shown in the given figure.

Step 2: Now with X as center and a suitable radius draw an arc on either side of the given line segment AB. Also, with Y as center and same radius as previous, draw an arc on either side of the given line segment cutting the arc drawn through point X at M as shown in the given figure.

Step 3: Join the point M and P as shown, and the line segment MP is the required perpendicular to AB through point P.

Let us see if the line segment MP constructed is actually perpendicular to AB or not.

Join M to the points X and Y as shown:

Thus, the constructed line segment MP is perpendicular to AB. Using the above construction, we can easily construct two perpendicular lines using compass and a ruler.

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