Question 817801
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Hi, 
To prove that ABCD is a parallelogram BY FIRST proving triangle ACD is congruent to triangle CAB: 
Use ASA Congruence Postulate
(Note: AC is congruent to itself & alternate interior angles of Transversal AC are Equal )
{{{drawing(400,400,-7,7,-2,10,
locate(-2,6.5,B), locate(-5.5,2,A), locate(2.5,2,D), locate(5,6.5,C),
green(line(-5,2,-2,6)), green(line(-2,6,5,6)),
green(line(5,6,2,2)), green(line(2,2,-5,2)),blue(line(-5,2,5,6))  )}}}