Question

draw a line segment 6.4 cm long and draw its perpendicular bisector. measure the length of each part​

Answer 1

a line segment 6.4 cm long

(i) Draw a line segment AB = 6.4 cm.

(ii) With centres A and B and with some suitable radius, draw arcs intersecting each other at S and R.

(iii) Join SR intersecting AB at Q. Then PQR is the perpendicular bisector of line segment AB.

Answer 2

$\bf\underline{\underline{\pink{Steps\:of\: construction:-}}}$

1) Draw a line segments AB = 6.4 cm.

2) With A s a centre and a radius equal to more than half of AB, draw two arcs,one above AB and other below AB.

3),With B as centre and the same radius, draw two arcs, cutting the previous drawn arcs at point C and D respectively.

4)Join CD, intersecting AB at point O.

Then, CD is the required perpendicular bisectors of AB at the point O.

On measuring, we find that

OA = 3.2 cm and OB = 3.2 cm

Also, ∠AOC = ∠BOC = 90°

$\bf\underline{\underline{\blue{Justification:-}}}$

Join AC, AD, BC and BD.

In ∆CAD and ∆CBD, we have

AC = BC (arcs of equal radii)

AD = BD (arcs of equal radii)

CD = CD (common)

∴∆CAD ≅ ∆CBD (S.S.S-criterian)

∴∠ACO = ∠BCO (c.p.c.t)

Now, in ∆AOC and ∆BOC, we have

AC = BC (arcs of equal radii)

∠ACO = ∠BCO (proved above)

CO = CO (common)

∴ ∆AOC ≅ ∆BCO (S.A.S-criterian)

Hence, AO = BO and ∠AOC = ∠BOC

But, ∠AOC + ∠BOC = 180° (linear pair axiom)

∴ ∠AOC = ∠BOC = 90°

Hence, COD is the perpendicular bisector of ∠AOB.