ABCD is a parallelogram with diagonal AC. If a line XZ is drawn such that XZ∥AB and cuts AC at Y then, findBXXC.
AZZD
In the Δ ABC,
AB∥XZ
⇒AB∥XY
∴ BXXC=AYYC....(1) [by BPT]
In parallelogram ABCD,
AB ∥ CD
AB ∥ CD ∥ XZ
In the Δ ACD,
CD ∥ YZ
∴ AYYC=AZZD....(2) [By BPT]
From 1 & 2,
BXXC=AYYC=AZZD
BXXC=AZZD