Posted by TUHITUHI on Wednesday, August 15, 2012 at 12:32pm.
You don't say, but seem to imply that AB=BD. That is, you haven't said anything about how far AB is extended.
It appears that DE is parallel to BC.
In triangle BCE and CBD,
BC = CB
angle BCE = angle CBE
CE = BD
So, by SAS, the triangles are congruent.
Thus, BE=CD
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