Here we will learn how to construct a perpendicular bisector of a line segment.
The perpendicular bisector of a line segment is the line that is perpendicular to the line segment at its mid-point.
In the adjoining Fig., \(\overleftrightarrow{PO}\) is the perpendicular bisector of \(\overline{AB}\) bisecting \(\overline{AB}\) at O i.e., \(\overline{AO}\) = \(\overline{BO}\)
Working Rules To Draw the Perpendicular Bisector:
Step I: Draw a line segment PQ.
Step II: Paste a strip of a transparent rectangular taps diagonally across the end-points P and Q as shown in the figure.
Step III: Repeat the process as in step-2 by placing another taps over P and Q just diagonally across the previous one. Thus, two strips cross at M and N.
Step IV: Join M and N to get \(\overline{MN}\) and \(\overline{PQ}\) as the required perpendicular bisectors of each other.
Working Rules To Draw the Perpendicular Bisector:
Step I: Draw a line segment AB of any length.
Step II: Using compass, draw an arc with A as centre and a radius more than half the length of \(\overline{AB}\)
Step III: With B as a centre and same radius as in step-II, draw another arc to intersect the previous arc at P and Q.
Step III: Join P and Q to get \(\overleftrightarrow{PQ}\). It cuts AB at O. This line PQ bisects the given line segment AB at O. i.e. \(\overline{AO}\) = \(\overline{BO}\)
What would happen?
In steps II and III above, what would happen, if we take less than half of the length as radius and draw arcs?
1. Draw a line segment AB of length 8 cm. Using compass, divide it into four equal parts.
Solution:
Step I: Draw a line segment AB = 8 cm and draw a perpendicular bisector using steps given in the Working Rules.
Step II: In step I, we have divided \(\overline{AB}\) into two equal parts \(\overline{AC}\) and \(\overline{BC}\) Similarly, draw the perpendicular bisectors of \(\overline{AC}\) and overline BC separately.
Now, we obtain four equal parts of \(\overline{AB}\)
i.e., \(\overline{AD}\) = \(\overline{CD}\) = \(\overline{CE}\) = \(\overline{BE}\) = 2 cm .
1. Draw a line segment of 8.5 cm and draw its perpendicular bisector.
2. Divide a line segment of length 8 cm into four equal parts using compass.
3. Draw a circle of radius 5 cm. Draw two chords on it. Constrct the perpendicular bisector of these chords. Where do they meet?
4. Draw a triangle. Construct three perpendicular bisectors on each of its side. Check whether all three bisectors meet at one point.
5. Divide a line segment of length 10 cm into four equal parts using compass.
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