Question : In $\Delta ABC$, two points $D$ and $E$ are taken on the lines $AB$ and $BC,$ respectively in such a way that $AC$ is parallel to $DE$. Then $\Delta ABC$ and $\Delta DBE$ are:
Option 1: Similar only if $D$ lies outside the line segment $AB$.
Option 2: Congruent only if $D$ lies outside the line segment $AB$.
Option 3: Always similar.
Option 4: Always congruent.
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Correct Answer: Always similar.
Solution :
We have, $D$ and $E$ are the points on $AB$ and $BC$. Such that $AC$ is parallel to $DE$.
In $\Delta ABC$ and $\Delta DBE$,
$\angle A=\angle D$ (Corresponding angle)
$\angle C=\angle E$ (Corresponding angle)
$\therefore \Delta ABC\sim\Delta DBE$ (by AA similarity)
Hence, the correct answer is Always similar.
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