In the figure, $A B ∥ D C$ and $A D ∥ B C$ Show that $△ A B C ≅ △ C D A$ .

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Solution

Consider $△ A B C$ and $△ C D A$
$∠ B A C = ∠ D C A$ ...(Alternate interior angles)
$A C = C A$ ...(Common side)
$∠ B C A = ∠ D A C$ (Alternate interior angles)
$△ A B C ≅ △ C D A$ ...(By ASA congruency)

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