In the given figure, if AD = BC and AD || BC, then prove that AB = DC.

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Solution

In $△ A C B$ and $△ C A D$ ,
$A D = B C$ [Given]
$∠ C A D = ∠ A C B$ [Alternate angles]
$C A = A C$ [common side]
$△ A C B ≅ △ C A D$ [SAS congruency]
$∴ A B = D C$ [CPCT]

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