ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that it cuts the side AD at point Z and XY $∥$ AB, then $\frac{B X}{X C} =$

\frac{A Y}{A C}

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\frac{D Z}{A Z}

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\frac{A Z}{Z D}

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\frac{A Y}{Y C}

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Solution

The correct options are
C $\frac{A Z}{Z D}$
D $\frac{A Y}{Y C}$
In the $Δ$ ABC,
AB $∥$ XZ
AB $∥$ XY
Therefore, $\frac{B X}{X C} = \frac{A Y}{Y C}$ ..........(1)
In parallelogram ABCD,
AB $∥$ CD
AB $∥$ CD $∥$ XZ
In $Δ$ ACD,
CD $∥$ YZ
Therefore, $\frac{A Y}{Y C} = \frac{A Z}{Z D}$ .........(2)
From 1 & 2,
$\frac{B X}{X C} = \frac{A Y}{Y C} = \frac{A Z}{Z D}$

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