Question

Draw a line AB equal to 6 cm. consrtruct a line XY parallel to AB at a distance of 4.5 cm. Now take a point anywhere above XY and draw a line PQ parallel to XY . Is AB also paralle

l to PQ?

Answer 1

Draw line AB of 6 cm.

Take any two points P and Q on AB.

Construct angle BPE = AQF=90°.

With P as the centre and radius equal to 4.5 cm cut PE at C.

With Q as the centre and radius equal to 4.5 cm cut QF at D.

Join CD to produce the line XY parallel to AB.

Take any point I on XY and Z above XY.

Join IZ.

Draw an arc cutting IZ and XY at L and M with centre I.

With centre Z draw an arc ON as shown in the picture.

Measure ML and an arc of same radius with centre N.

Join PQ which is parallel to XY.

So if AB is parallel to XY and XY is parallel to PQ , then AB is parallel to PQ.