Question 476826: Prove that the diagonals of a rhombus are perpendicular bisectors of one another. (Formal Proof)
I don't understand where to get started. I drew a picture, but that will not help me prove this theorem....
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Draw the rhombus and its diagonals:
ABCD is a rhombus, meaning that AB = BC = CD = DA. You will have a bunch of isosceles triangles, so lots of angle chasing. One way to prove it is to claim that triangles DAB and BCD are congruent, via SAS, and they are isosceles, so angles ABD, BDA, CDB, and DBC are all congruent. Then we know that triangles ABE and CBE are congruent, by SAS (since angles ABD and DBC are =), so angle AEB = angle CEB = 90, and AE = EC. The same logic applies with the other diagonal.
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