WHAT IS A PERPENDICULAR BISECTOR

PERPENDICULAR BISECTOR

A perpendicular bisector is a line that divides a given line segment into equal parts and forms 90° angles at the intersection points. The term bisect itself means dividing equally. Bisectors intersect the line segment and form angles of 90 degrees on it. 

It is very easy to construct a perpendicular bisector using a ruler and compass.

PROPERTIES OF A PERPENDICULAR BISECTOR

1. Perpendicular bisectors divide the segment into equal parts so any point that is on the perpendicular bisector is equidistant from both the ends of the segment.
   
   
2. There can only be one perpendicular bisector for a given line segment.
   
   
3. A perpendicular bisector makes an angle of 90 degrees with the line that it bisects.
   
   
4. When we draw the three perpendicular bisectors of a triangle, the meeting point is called the circumcentre. It is different for different types of triangles. The circumcentre is inside the triangle in case of an acute triangle, outside of the triangle in case of an obtuse triangle and at the hypotenuse in case of right-angled triangles.

HOW TO CONSTRUCT A PERPENDICULAR BISECTOR FOR A LINE SEGMENT

Let us learn how to construct a perpendicular bisector of a line segment.

Step 1: Draw a line segment PQ of any length.

Step 2: Place the compass at point P taking it as a centre and more than half of the line segment PQ as width, draw two arcs one above the line and one below the line.

Step 3: Repeat the step above with Q as the centre.

Step 4:  Label the points of intersection as A and B.

Step 5:  Join the points A and B. This line segment AB is the perpendicular bisector. AB intersects the line segment PQ at its midpoint.

PERPENDICULAR BISECTOR OF A TRIANGLE

The perpendicular bisector of a triangle is a line segment that bisects the side of a triangle and passes through the midpoint of the side. It is perpendicular at the midpoint of the side of the triangle. We can draw perpendicular bisectors for all three sides of a triangle. When we draw the three perpendicular bisectors, they meet at a point which is called the circumcentre of the triangle. 

It is very easy to draw the perpendicular bisector of a side of a triangle if we know how to draw one for a line segment. We have a triangle ABC and we want to draw the perpendicular bisector of the line segment BC. We will do so in the following steps –

Step 1: Take B as a centre and more than half of the length of BC as radius. Use the compass to draw arcs above and below the line segment BC and repeat the same process with C as the centre. We can label the points as P and Q. When we join P and Q, we get the perpendicular bisector of one side of the triangle BC. 

Step 2: Repeat the process for the other sides AB and AC to get the perpendicular bisectors of the other two sides. 

The point of intersection of the respective perpendicular bisector on each side is the midpoint of that side. 90° angle is formed at the midpoints.