Given: segment ac is perpendicular to segment bd prove: δacb ~ δecd reflect δecd over segment ac. this establishes that ∠acb ≅ ∠e'c'd'. then, this establishes that therefore, δacb ~ δecd by the aa similarity postulate. translate point e' to point a; ∠e'd'c' ≅ ∠abc translate point d' to point a; ∠e'd'c' ≅ ∠bac translate point d' to point b; ∠d'e'c' ≅ ∠bac translate point e' to point a; ∠d'e'c' ≅ ∠bac