Can a trapezoid be a parellelogram?

You would think so, but a trapezoid is defined as having exactly one pair of parallel sides. So an isosceles trapezoid having 2 pairs would be breaking the rules.

However, there are some math experts who define trapezoid as having at least one pair of parallel sides. In this case it can happen.

The most important thing is to know which definition is being used. That will directly answer the question.