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Construction of Bisectors of Line Segments

Construction of Bisectors of Line Segments

 


1. Let AB be the given line segment.
2. With A and B as centres and radius more than half of AB draw arcs on either side of AB. Let the arcs cut at points C and D.
3. Join CD.
4. CD is the perpendicular bisector of AB.

Let AB be the given line segment of length, say, 6cm. We have to find a point O on AB such that AO = OB.
 

1. Draw a line segment AB = 6cm.
2. With A as centre and radius more than half of AB, cut arcs on both sides of AB.
3. With B as centre and the same radius, draw arcs to cut the previous arcs at C and D.
4. Join CD, cutting AB at O.

Then O bisects AB.
Check to see if AO = OB. Measure angles AOC and BOC. You will find that
AOC = BOC = 90°. Therefore CD is the perpendicular bisector of AB.
 





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