Draw a line segment AB of 4cm in length . Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?

Draw a line segment AB of 4cm in length . Draw a line perpendicular to

1.	Draw a line segment AB of 4cm in length . Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?
Answer» Solution :To DRAW a line perpendicular to `AB` through `A` and `B`, respectively. Use the following steps of construction. (i) Draw a line segment `AB = 4cm`. (ii) Taking `A` as centre and radius more than `(1)/(2)AB` (i.e., 2 cm) draw an arc say it intersect `AB` at `E`. (iii) Taking `E` as centre and with same radius as above draw an arc which intersect previous arc at `F`. (iv) Again, taking `F` as centre and with same radius as above draw an arc which intersect previous arc (obtained in step ii) at `G`. (v) Taking G and F are CENTRES, draw arcs which intersect each other at H. (vi) Join AH. Thus , AX is perpendicular to AB at A. Similarly, draw `BY bot AB` at B Now, we know that if two LINES are parallel , then the angle between then will be `0^(@) or 180^(@)` . Here, `angleXAB = 90^(@) [becauseXA bot AB]` and `angleYBA = 90^(@) [becauseYB bot AB]` `:.angleXAB + angleYBA = 90^(@) + 90^(@) = 180^(@)` So, the lines XA and YB are parallel. [since, it sum of interior angle on same side of transversal if `180^(@)` , then the two lines are parallel]