Perpendicular Bisector

While working with practical geometry, you will often find the application of perpendicular bisectors; say when you are asked to draw an isosceles triangle, or when you have to determine the center of a circle, etc. So here, in this article, we learn how to construct a perpendicular bisector of a line segment.

What is a Perpendicular Bisector?

Two lines are said to be perpendicular to each other when they intersect in such a way that they form 90 degrees with each other. And a bisector divides a line into two equal halves. Thus, when we talk about the perpendicular bisector of a line segment AB, it implies:

  • It divides AB into two equal halves or bisects it.
  • It make right angles with (or is perpendicular to) AB.
  • Every point in the perpendicular bisector is equidistant from point A and B.

How to Construct a Perpendicular Bisector?

You will require a ruler and compasses. The steps for the construction of a perpendicular bisector of a line segment are:

  • Step 1: Draw a line segment PQ.
  • Step 2: Adjust the compass with length a little more than half of the length of PQ.
  • Step 3: Place the compass pointer at point P and draw arcs above and below the line.

Perpendicular Bisector

  • Step 4: Keeping the same length in the compass, place the compass pointer at point Q. Similarly, draw two arcs above and below the line keeping the compass pointer at Q.

Perpendicular Bisector

  • Step 5: Mark the points where the opposite arcs cross as X and Y.

Perpendicular Bisector

  • Step 6: Using a ruler, draw a line passing across X and Y.

Perpendicular Bisector

The perpendicular bisector bisects PQ at a point J, that is, the length PJ is equal to JQ. And the angle between the two lines is 90 degrees.

To learn more about the perpendicular bisector of a line segment, download Byju’s The Learning App.


Practise This Question

If AB is perpendicular to CD and PQ is perpendicular to AB, which of the following is/are true?