Rely on Maths lecturer? Think twice!

I was disappointed with my Maths lecturer...... If a student did this mistake, i would hav forgiven the person but this is a maths lecturer! The test question that she discussed with us goes like this:(not exactly but the idea is the same)
Line 1 & line 2 intersect at point B. Point A is on line 1 while point C is on line 2. ABCD is a parallelogram.(also the numerical info is given but there's no need to mention it since we wont use it here)
(i) Show that AB=BC.
(ii) Find the coordinate of point D.

After doing the 1st part of the question, my lecturer suggested the following diagram for part (ii).
She said, 'there r 4 possibilities of how u could draw point D but we'll just draw one as a guide.'

My goodness! Nearly fainted when she proposed that diagram. But i thought, maybe she just was just careless. So i kept quiet n let it be... However, it was noticed by charles who then pointed it out(say loud loud some more), "teacher, point D is supposed to be at the other side!(he meant solution 1)". But to my surprise, she said, "as i've told u just now, there r 4 possibilities of how u could draw point D n this is one of them. of course u can draw that way too. but we'll discuss this diagram according to my diagram."

YES, THERE R 4 DIAGRAM OF SOLUTIONS TO POINT D BUT THE ABOVE ONE IS DEFINITELY NOT ONE OF THEM! The solutions r as the following:



I kept quiet for the second time. I know she wasn't gonna admit that she was wrong. But Sze Chiang n Charles just couldn't get over it n they argued with her AGAIN. My jaw dropped when she said, "It is not necessary to follow the order of ABCD when u label a polygon." This STUPID statement came out from a Maths lecturer! She meant the diagram below is absolutely correct!Hell, it is altogether WRONG! and a HUGE MISTAKE to be made by a lecturer! A person good in Maths will never draw it this way, simply because it is WRONG! In the question part (i), it's already mentioned that AB and BC r the sides of the parallelogram, so how on earth could we obtain the above diagram? Another argument point: if she had proposed point D to be as in her diagram, ABCD should be this:
Let me remind u the definition of a parallelogram. According to Oxford dictionary, parallelogram is a flat shape with 4 straight sides, the opposite sides being parallel and equal to each other. And this is what the dictionary showed for parallelogram(the middle one):That z-shaped thing was not even close to a polygon, let alone a parallelogram!
At the end of the day, we went back late, thanks to Charles n Sze Chiang who never gav up(gav up in the end too) explaining to the lecturer. It dawned on me that she was not careless; she didn't even know that she was wrong, and the worse is she insisted she was right. All the while i've been keeping quiet cos i certainly don't want to catch the bus late!
This is the forever only correct way to label a polygon:
Well, the conclusion is, she was wrong, n point D can't be there as she proposed. But i could not tolerate with such mistake. How could a lecturer teach her student to label a parallelogram that way? Ugh.... U may think that i'm too emo, but i refuse to let ppl insult my beloved Mathematics!