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.
- 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.
- Step 5: Mark the points where the opposite arcs cross as X and Y.
- Step 6: Using a ruler, draw a line passing across X and Y.
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.
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