prove opposite angles of parallelogram are congruent
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lets consider quadrilateral ABCD as a parallelogram
since ABCD is a parallelogram, its opposite sides and are parallel and equal
Therefore, AB//CD and BC//AD
AB=CD and BC=AD
Now construct a diagonal BD
In triangle ABD and triangle BCD
ABD=BDC-(alternate angles)
ABD=BDC-(alternate angles)
BD=BD-(common side)
triangle ABD congruent BCD-(A-S-A test)
therefore now all the opposite angles will be equal by property of congruent angles
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