July 25, 2017 note: I have just received word that NYSED has deemed all 4 answers to be granted credit for this question.
Here is a question from last months new York State Regents Exam in Geometry (Common Core)
This question, to be answered best, requires you to identify three which are sufficient. The one left over would be the answer. Wouldn't it?
The Regents "powers that be" have decreed that choice "2" is the correct answer. They are wrong. There is no correct answer: all 4 choices are sufficient for the task.
A key item in analyzing this question is recognizing that point C in the diagram is between points A and E and between points B and D. This information is embedded in the diagram. Should a blind student be taking this test, this information must be verbally communicated (maybe using the sense of touch is possible, but I will not deal with that here.)
If the diagram has been totally omitted from the question, all bets are off. As a matter of fact, a better question would have been to leave out the diagram and leave out the word "not" in the question.
Although this does not constitute a proof, it illustrates what a proof for choice "2" would be dealing with. I did not use the same point names, but the lengths are correct. Points A, B, E can be dragged.
A more detailed proof has been written and the link can be found at https://www.change.org/p/nysed-mark-q-24-on-the-june-2017-geometry-regents-as-correct
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