From the figure,

In the Δ ABC and inΔ ACD, we have

AB = CD  (given)

AD = BC  (given)

AC = AC  (Common side)

Hense, Δ ABC ≅ Δ ACD

So, ∠DAC = ∠BCA  {both opposite equal sides DC and AB}

CD || AB  {since alternate angles are equal}

∠DCA = ∠CAB  {both opposite equal sides AD and BC}

So, AD || BC {since alternate angles are equal}

Since opposite sides of quadrilateral are parallel,

So ABCD is a parallelogram.