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Perpendicular Bisector of a Line Segment

A line that is perpendicular to a line segment and also divides the line segment into two equal
parts is called a perpendicular bisector of the line segment.

Here, line l is the perpendicular bisector of the line segment PQ of length 6 cm as l
A
PO = OQ = 3 cm and ∠AOP = 90°.

Let us draw a perpendicular bisector of a line segment PQ = 7 cm.
P 3 cm O 3 cm Q
Steps of construction:
1. Draw a line segment PQ of length 7 cm. B

2. Take P as centre and with radius more than half of PQ, draw arcs above and below the line PQ.
3. Now take Q as centre and draw arcs above and below the line PQ with the same radius as
taken before.
4. Both the arcs intersect at points S and N respectively.

5. Join S and N that intersect PQ at M.
Verify: Measure PM and QM.

You will find PM = QM.
and ∠SMQ = ∠SMP = 90°
Hence, SM is the perpendicular bisector of PQ.

Maths Talk

Take a piece of paper. Fold it down from the middle and make the crease.
Fold the paper once again from the middle in the other direction.
Make the crease and open out the page.
Are the two creases perpendicular to each other? Discuss

Construction of Perpendiculars Using Ruler and Set Squares

Construction of a Perpendicular Through a Point P on the Line l

Let us construct a perpendicular through a point P on the line l.
Steps of construction:

1. Draw a line l and a point O somewhere on the line l.

O
l
2. Place a ruler with one of its edges along the line l.

O
l
1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm 15
inches 1 2 3 5

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