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Condition for Two Lines to Be Parallel

In figure, if...

Question

In figure, if AB $| |$ DC and E is mid point of AC, then prove that E, will be the mid-point of side BD.

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Solution

$A B | | C D ⟹ ∠ B = ∠ D ∠ A = ∠ C ∠ E = ∠ E (V e r t . O p p .) ⟹ A B E \sim C D E ⟹ \frac{A E}{E C} = \frac{B E}{E D} \frac{B E}{E D} = \frac{1}{1} B E = E D$
$⟹ E$ is mid point of $B D$

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