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`I always thought opposite sides were congruent` you are correct

Does that apply to angles too or just sides?

Parallelogram ABCD
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more properties are listed here
https://en.wikipedia.org/wiki/Parallelogram

At first I said that C was the answer, "its consecutive angles are congruent" but that was wrong

example of a particular parallelogram
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|dw:1438747418593:dw|

120+60 = 180. Consecutive angles are supplementary ?

correct