6) If line segment a = 4cm, then construct a line segment equal to 2a.
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1. Step-by-step explanation:

   To draw a line perpendicular to AB through A and B, respectively. Use the following steps of construction.

   1.Draw a line segment AB = 4 cm.

   2.Taking 4 as centre and radius more than ½ AB (i.e., 2 cm) draw an arc say it intersect AB at E.

   3.Taking E as centre and with same radius as above draw an arc which intersect previous arc at F.

   Again, taking F as centre and with same radius as above draw an arc which intersect previous arc (obtained in step ii) at G.

   5.Taking G and F are centres, draw arcs which intersect each other at H.

   6.Join AH . Thus, AX is perpendicular to AB at A. Similarly, draw BY ⊥ AB at B.

   Now, we know that if two lines are parallel, then the angle between them will be 0° or

   180°.

   Here, ∠XAB = 90° [∴ XA ⊥ AB]

   and ∠YBA = 90° [ ∴ YB ⊥ AB]

   ∠XAB+ ∠YBA = 90° + 90° = 180°

   So, the lines XA and YS are parallel.

   [since, it sum of interior angle on same side of transversal is 180°, then the two lines are

   parallel]

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