Theory:

In your earlier classes, you learned about the line segments and basic types of angles. Now in this lesson, we are going to construct a following get proper visual understanding.
  • Perpendicular bisector of a line segment
  • Angle bisector of an angle
  • Construct of special angles without protractor
The construction of perpendicular bisector of a line segment:
 
Make a note of the following steps to construct a perpendicular bisector of the line segment \(AB = 10 cm\).
 
Step 1: Draw a line and mark two points \(A\) and \(B\) on it. That is, \(AB = 10cm\).
 
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Step 2: Make \(A\) as centre and radius more than half of the length of \(AB\), draw two arcs of same length, one above \(AB\) and one below \(AB\).
 
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Step 3: Now take \(B\) as centre, draw two arcs with the same radius to cut the arcs drawn in step \(2\). Mark the points of intersection of the arcs as \(C\) and \(D\).
 
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Step 4: Then, join \(C\) and \(D\). The line \(CD\) will intersect \(AB\). Mark the point of intersection as \(O\). \(CD\) is the required perpendicular bisector of \(AB\). Now measure the distance between \(A\) and \(O\) and \(O\) and \(B\). We have \(AO = OB\) \(= 5 cm\).
 
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Thus, we have constructed the perpendicular bisector of \(AB\) and this perpendicular bisector divides the line \(AB =10 cm\) two parts \(AO\) \(= OB\) \(= 5 cm\).