The proofing that ABCD is a parallelogram is done using parallelogram side theorem.
What is parallelogram side theorem?
parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.
As, ABCD is a parallelogram.
So, BAC and DCA are alternate interior angles.
Also, AB||CD and BC||DA.
then, BCA and DAC, are alternate interior angle.
Now In ABC and CDA
BAC= DCA (proved above)
BCA= DAC (proved above)
AC= AC (Common)
By ASA congruency criteria,
ΔABC≅ ΔCDA
Hence, AB= CD and BC= DA (cpctc)
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