Consider ΔABC,
AB∥XY
∴BXXC=AYYC...(i) (By Basic proportionality theorem)
Consider parallelogram ABCD, AB || CD(Opposite sides of a parallelogram areparallel)
⇒AB∥CD∥XZ
Consider ΔACD,
CD∥YZ
∴AYYC=AZZD...(ii) (By Basic proportionality theorem)
From (1) and (2),
BXXC=AYYC=AZZD