TITLE: Dissection of square into triangles
QUESTION [12 upvotes]: Prove that a square cannot be dissected into an odd number of triangles of equal area.
Got to read about the question and its history in "Algebra and Tiling Homomorphisms in the Service of Geometry by  Sherman Stein and Sándor Szabó 
quite an interesting question, neither my doubt nor my homework, just want to see the various ideas that people here would come up with it.
edit: the proof i have seen involves higher mathematics which I have not yet completed in my college courses. Posting here mainly to see if anyone can come up with an idea that would be understood by me or a similar pre college student

REPLY [4 votes]: The only proof I know of is the $p$-adic one due to Monsky. 
EDIT: I found some confirming evidence at Math Reviews. The review of Charles H. Jepsen and Paul Monsky, Constructing equidissections for certain classes of trapezoids, Discrete Math. 308 (2008), no. 23, 5672–5681, MR2459386 (2009h:05053), written by Sherman Stein, says, in part, 
The simple question, "Can a square be cut into an odd number of triangles of equal areas,'' raised some forty years ago, has generated more questions, only some of which have been answered. The answers so far have used valuations and algebraic integers.