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Question

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?


A

CBBA=PQQR

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B

ABBC=PQQR

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C

ABQR=PQBC

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D

ABPQ=PQBC

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Solution

The correct option is B

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


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