Which pair of triangles can be proved congruent by the sas postulate? given: x is the midpoint of both ad and be a. ∆acd and ∆ecb b. ∆ade and ∆abe c. ∆abx and ∆edx

This is another one for my "impossible geometry" file.

If X is the midpoint of both AD and BE, then ABDE is a parallelogram, and point C cannot exist.

The congruent segments are
   BX ≅ EX
   AX ≅ DX
Of course, vertical angles AXB and DXE are congruent.
Then, by SAS, the congruent triangles are
   ΔAXB ≅ ΔDXE
or
   ΔABX ≅ ΔDEX

Selection C is close, but has points D and E swapped. The figure is misleading, which may be a contributor to the problem.