Perpendicular Bisector

What is a Perpendicular Bisector?

A perpendicular bisector can be defined as a line segment which intersects another line perpendicularly and divides it into two equal parts. 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, a perpendicular bisector of a line segment AB implies that it intersects AB at 90 degrees and cuts it into two equal halves.

Properties of a Perpendicular Bisector

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

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. Below are the steps to construct a perpendicular bisector of a line using a compass and a ruler.

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.
Construction of Perpendicular Bisector : Place the compass pointer at point P and draw arcs above and below the line.

Construction of Perpendicular Bisector: Step 3

  • 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.
Construction of Perpendicular Bisector: Keeping the same length in the compass, place the compass pointer at point Q and draw two arcs above and below the line.

Construction of Perpendicular Bisector: Step 4

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

Construction of Perpendicular Bisector: Step 5

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

Construction of Perpendicular Bisector: Step 6

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.

More Topics Related to Perpendiculars

Frequently Asked Questions

What does a Perpendicular Bisector Mean?

A perpendicular bisector can be defined as a line segment which bisects another line segment at 90 degrees. In other words, a perpendicular bisector intersects another line segment at 90° and divides it into two equal parts.

Can a Perpendicular Bisector be a Median of a Triangle?

Yes, a perpendicular bisector can be a median of a triangle. A median is defined as a line segment from a vertex of a triangle to the midpoint of the side opposite to that vertex. So, if the median joins the opposite side at 90 degrees, it will be the perpendicular bisector of that side. For example, for an equilateral triangle, the medians are always perpendicular bisectors.

What is the Point at Which the Perpendicular Bisectors of a Triangle Meet Called?

The point at which the perpendicular bisectors of a triangle meet is known as the circumcenter of the triangle and it is equidistant from all the vertices.

What is Perpendicular Bisector Theorem?

Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment’s endpoints.

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