This post is dedicated to proving the diagonals of a rhombus are perpendicular. To complete this or any proof, it is good to make a plan. In this case, I am going to establish that the two triangles on the top of the rhombus are congruent. This is seen in steps 2 through 4 of the proof below. Next, I show that angles AEB and CEB right angles, which is modeled in steps 6 through 8. That is enough to state the diagonals of a rhombus are perpendicular.
I encourage you to click on the image to see it at full size. It looks much better at full size. I scanned the piece of notebook paper that I work this proof out on and messed around in photoshop.