Identification of a quadrilateral as a trapezoid, rectangle, or square Yesterday I was tutoring a student, and the following question arose (number 76):

My student believed the answer to be J: square. I reasoned with her that the information given only allows us to conclude that the top and bottom sides are parallel, and that the bottom and right sides are congruent. That's not enough to be "more" than a trapezoid, so it's a trapezoid. 
Now fast-forward to today. She is publicly humiliated in front of the class, and my reputation is called into question once the student claims to have been guided by a tutor. The teacher insists that the answer is J: square ("obviously"... no further proof was given).


*

*Who is right? Is there a chance that we're both right? 

*How should I handle this? I told my student that I would email the teacher, but I'm not sure that's a good idea. 

Of course, you are right. Send an email to the teacher with a concrete example, given that (s)he seems to be geometrically challenged. For instance, you could attach the following pictures with the email, which are both drawn to scale. You should also let him/her know that you need $5$ parameters to fix a quadrilateral uniquely. With just $4$ pieces of information as given in the question, there exists infinitely many possible quadrilaterals, even though all of them have to be trapezium, since the sum of adjacent angles being $180^{\circ}$ forces the pair of opposite sides to be parallel.
The first one is an exaggerated example where the trapezium satisfies all conditions but is nowhere close to a square, even visually.
The second one is an example where the trapezium visually looks like a square but is not a square.
Not only should you email the teacher, but you should also direct him/her to this math.stackexchange thread.
Good luck!

EDIT
Also, one might also try and explain to the teacher using the picture below that for the question only the first criterion is met, i.e., only one pair of opposite sides have been made parallel.

