# Let $l$ be a line and $P$ be a point not on $l$. Through $P$, draw a line $m$ parallel to $l$. Now join $P$ to any point $Q$ on $l$. Choose any other point $R$ on $m$. Through $R$, draw a line parallel to $PQ$. Let this meet $l$ at $S$. What shape do the two sets of parallel lines enclose?

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Steps of construction:
• Draw a line l, take a point A on it.
• Take a point P, not on l, and join A to P.
• Taking A as a center and with a convenient radius draw an arc cutting l at B and AP at C.
• Taking P as the center and with the same radius as before, draw an arc DE to intersect AP at F.
• Adjust the compass up to the length of BC and without changing the opening of the compass and taking F as the center, draw an arc to intersect the previous drawn arc DE at point G.
• Join P to point G to draw a line m. Line m will be parallel to l.
• Join P to any point Q on line l. Choose another point R on line m.
• Similarly, a line can be drawn through point R and parallel to PQ using the above steps. Let it meet line l at point S.
Thus, line PQ is parallel to RS. The shape enclosed by these two sets of parallel lines is a parallelogram PQRS with PR || QS and PQ || RS.
Updated on 10-Oct-2022 13:35:45