Is this a parallelogram? How do you tell or not?

The markings on the short segments indicate that the uppermost triangle is congruent to the lowermost triangle (by "SAS"), so the uppermost and lowermost sides of the whole figure are equal to one another.

Similarly, the leftmost and rightmost triangles are congruent (by "SAS" again), so the leftmost and rightmost slanty sides on the outside are equal to one another.

A figure with a pair of equal sides alternating with another pair of equal sides is a parallelogram.  You could also argue this by stepping around the figure and finding that the angles to get you from the top side to the bottom side have to add up to 180.  Etc.

Yes it is not a square or rectangle, but still has two sets of parallel sides.