In the follow diagram, lines l, m and n are parallel to each other. Two transversals p and q intersect the parallel lines l, m and n at points A,B,C and P,Q,R respectively as shown below.
Which of the following is correct?
ABBC=PQQR
In the given figure, l||m||n
Construction: Join AR which intersects BQ at D.
In ΔACR
BD||CR (∵m || n)
ABBC=ADDR...(i)
(By basic proportionality theorem)
Similarly in ΔARP,
DQ || AP(∵l || m)
PQQR=ADDR...(ii)
(By basic proportionality theorem)
From (i) and (ii),
ABBC=PQQR