Two sides and the included angle of △ BCA are congruent to two sides and the included angle of △ DCE. Thus, △ BCA≅ △ DCE by the Side-Angle-Side Theorem. To prove that DE ≅ DC, we need to prove that ∠ E ≅ ∠ DCE. Once we know this, DE ≅ DC because △ DCE is isosceles and the corresponding angles
are congruent.
Because corresponding parts of corresponding triangles are congruent,
If ∠ A ≅ ∠ BCA, then ∠ E ≅ ∠ DCE.
Therefore, the additional statement ∠ A ≅ ∠ BCA is required. The correct choice is F.
