CONSTRUCTION OF PERPENDICULAR BISECTOR OF A LINE SEGMENT

In this section, you will learn how to construct perpendicular bisector of a line segment. 

Key Concept - Perpendicular Bisector

The line drawn perpendicular through the midpoint of a given line segment is called the perpendicular bisector of the line segment.

To construct a perpendicular bisector of a line segment, you must need the following instruments.

1. Ruler

2. Compass

The steps for the construction of a perpendicular bisector of a line segment are :

Step 1 :

Draw the line segment AB. 

Step 2 :

With the two end points A and B of the line segment as centers and more than half the length of the line segment as radius draw arcs to intersect on both sides of the line segment at C and D.

Step 3 :

Join C and D to get the perpendicular bisector of the given line segment AB.

In the above figure, CD is the perpendicular bisector of the line segment AB.

This construction clearly shows how to draw the perpendicular bisector of a given line segment with compass and straightedge or ruler.

This bisects the line segment (That is, dividing it into two equal parts) and also perpendicular to it. 

Perpendicular Bisector in a Triangle

The perpendicular bisector of a triangle is a line which is passing through the mid point of the side and also perpendicular to that side. 

Step 1 :

Draw the triangle ABC. 

Step 2 :

Select one the sides of the triangle, say AC

With the two end points A and C of the side AC as centers and more than half the length of the side AC as radius draw arcs to intersect on both sides of the side AC and join the points of intersection of the arcs.

Using the steps explained above, in the above triangle ABC, perpendicular bisector is drawn to the side AC.

Similarly we can draw perpendicular bisectors to the sides AB and BC as given below. 

So, every triangle will have three perpendicular bisectors.

Key Concept - Circumcenter

The point of concurrency of the perpendicular bisectors of the three sides of a triangle is called the circumcenter and is usually denoted by S.

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