Page 202 - Maths Class 06

Step 5. With out dis turb ing the open ing, place the pointer at l
A B
point B on the l and draw an arc cut ting the line l at C. C
Fig. 14.19
Step 6. AC is the re quired line seg ment whose length is equal
to the sum of the lengths of line seg ments AB and BC i e. ., AC = AB + BC.

Construction of a Perpendicular Bisector

A line which is perpendicular to a given line segment (AB) and divides it into X
two equal halves, i e. . AO = OB is called the perpendicular bisector of AB.
In the above Fig. 14.20, XY is the perpendicular bisector of AB, since 90°
A B
AO = OB and ÐXOB = 90°. O

Y
Fig. 14.20
To Draw a Perpendicular Bisector of a Line Segment
Con struc tion : Draw the per pen dic u lar bi sec tor of a line seg ment AB = 5 cm us ing a ruler and a pair of
com passes.

Step 1. Draw a line seg ment AB of length 5 cm.

A 5 cm B
Fig. 14.21

Step 2. Tak ing A as the cen tre and with any ra dius more than half A B

of AB, draw an arc on ei ther side of AB.

Fig. 14.22

C

Step 3. Sim i larly, tak ing B as the cen tre and ra dius as in step 2, draw
an other arc on ei ther side of AB in ter sect ing the pre vi ous arcs at A O B
C and D.

D

Fig. 14.23
Step 4. Join C and D cross ing AB at O.
Hence, CD is the required perpendicular bisector of line segment AB.

Ver i fi ca tion : Mea sure AO and OB. We find the mea sure ment of AO = OB
and also ÐCOB = ÐCOA = 90°.

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