There are many such shapes. Any polygon with an even number of sides can have opposite sides that meet the above requirements.
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Any polygon with 2n sides (n integer) where opposite sides are parallel, will have its opposite angles congruent.
Parallelogram opposite sides are congruent opposite sides parallel
no
If two opposite sides are congruent in length and direction then they are parallel sides. THat would mean the other two sides are congruent making 4 parallel sides or a parallelogram
No. The congruent sides need not be parallel.