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Thales Theorem

ABCD is a par...

Question

ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that it cuts the side AD at point Z and $X Y ∥ A B$ , 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 $Δ A B C$ ,
$A B ∥ X Z$
$A B ∥ X Y$
Therefore, $\frac{B X}{X C} = \frac{A Y}{Y C}$ ..........(1)
In parallelogram ABCD,
$A B ∥ C D$
$A B ∥ C D ∥ X Z$
In $Δ A C D$ ,
$C D ∥ Y Z$
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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