that (unintentionally) tricky geometry problem
(I can't show you the diagram, alas, but I can describe it well enough that you can probably draw it yourself:)
There is a plane E (lying flat).
In the plane are points A, B, and C.
A, B, and C form a triangle, with B "closest" to us, A at back left, and C at back right. In the diagram, the triangle appears approximately equilateral (but don't trust those apparent dimensions or angles).
Draw line segments AB, BC, and (dotted 'cause it's in back) AC.
Point H lies on segment AC.
Point D is not in plane E, it's "above" it, directly (?) over point H.
Draw (dotted) line segment DH.
Draw line segments AD, BD, and CD to complete a picture of a tetrahedral pyramid.

In this figure, points A, B, C, and H are in plane E.
AD is perpendicular to AB.
BC is perpendicular to CD.
DH is perpendicular to AC.
AC is perpendicular to CB.
Which segment and which plane are perpendicular?
(a) DH and plane E
(b) AD and plane E
(c) AB and plane ADC
(d) BC and plane ADC

(Keep in mind the theorem that "If a line is perpendicular to two distinct lines (or line segments) that lie in a plane and that pass through its foot (the point of intersection between the line and the plane), then the line is perpendicular to the plane." Also, any three noncollinear points determine a plane.)

Now, I took this problem from a set (with no answer key) in which it was possible to have more than one choice correct. However, I didn't tell the students that, because when I made the test on Thursday night, I was sure there was only one correct answer. Indeed, there is one definitely correct answer and two that are definitely wrong. But the other choice? Well, that got complicated...

(Solution tomorrow. I'll let y'all have fun with it for now. :-)
(ultimatepsi was able to figure it out over the phone while at a party, because she's full of awesome.)