Best answer gets

which of the following completes the proof?

triangles abc and edc are formed from segments bd and ac, in which point c is between points b and d and point e is between points a and c.

given: segment ac is perpendicular to segment bd

prove: δacb ~ δecd

reflect δecd over segment ac. this establishes that then, translate point e' to point a. this establishes that therefore, δacb ~ δecd by the aa similarity postulate.

∠abc ≅ ∠e'd'c'; ∠e'd'c' ≅ ∠abc
∠acb ≅ ∠e'c'd'; ∠d'e'c' ≅ ∠bac
∠acb ≅ ∠e'c'd'; ∠e'd'c' ≅ ∠abc
∠abc ≅ ∠e'd'c'; ∠d'e'c' ≅ ∠bac