Construct A Perpendicular BisectorA perpendicular bisector of a line segment AB is a line that divides the line AB into two equal parts at a right angle.
Example : Construct a perpendicular bisector of the given line segment AB.
Solution: Step 1 : Stretch your compasses until it is more then half the length of AB. Put the sharp end at A and mark an arc above and another arc below line segment AB.
Step 2 : Without changing the width of the compasses, put the sharp end at B and mark arcs above and below the line segment AB that will intersect with the arcs drawn in step 1.
Step 3 : Join the two points where the arcs intersect with a straight line. This line is the perpendicular bisector of AB. P is the midpoint of AB.
The above construction can also be used to construct an isosceles triangle or a rhombus. For example,
We have constructed 4 isosceles triangles; AQB, ARB, QAR and ARB. We have also constructed a rhombus AQBR.
The following video shows how to construct a perpendicular bisector of a line
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