In △ABC, D is the mid-point of side BC. A student attempted to prove that △ABD is congruent to △ACD using the following steps:
“AB=AC (given), BD=CD (since D is the mid-point of BC), ∠BAD=∠CAD (common) ⇒ △ABD≅△ACD by SAS.”
(i) Point out the specific error in the student's reasoning.
(ii) Write a correct proof to establish the congruence of △ABD and △ACD, clearly stating the criterion applied.
(iii) After proving congruence, state any two pairs of corresponding parts of the triangles that are equal.