In this question, Greg got rid of the last two options with trapezoids because he said trapezoids should have only 1 pair of parallel lines and in the video solution he mentions only C as the correct option. But the ETS math review guide mentions ‘at least one pair’. If we go according to ETS guide, then the option D is also a possible answer.
Here’s my thought process:

Even though the math review pdf says “at least one”, the definition of a trapezoid never mentions anything about the sides of the length. unless its an isosceles trapezoid, but in this case they haven’t included that.

So even though square is a possibility, so is a rectangle.
That being said the last option would not be correct.
Hope this helps.
If you make two parallel sides in a trapezoid then it becomes a parallelogram
https://en.wikipedia.org/wiki/Trapezoid
Yea I actually wanted to say the second last option.
But again it can either be a rhombus or a square
A rhombus need not be a square (@iori.yagami’s diagram is misleading since it shows four right angles, and a trapezium with four equal sides and angles is a square).
I drew a rectangle not square
But a trapezium with four equal sides cannot be a rectangle.
OK, you meant option E. I meant D.