Final answer:
To ascertain that two quadrilaterals are congruent, one needs to show that all corresponding sides are equal in length, which satisfies the condition for congruence.
Step-by-step explanation:
To argue that two quadrilaterals are congruent, a minimal set of conditions must be met, beyond just having the same area. Option A suggests that all sides of one quadrilateral are equal in length to the sides of the other quadrilateral, which is a valid condition for congruence. Option B references equal interior angles, but this alone cannot ensure congruence without the presence of equal sides because quadrilaterals can have the same angle measures but different side lengths. Option C involves the diagonals, stating that the diagonals of one quadrilateral bisect the diagonals of the other quadrilateral. This could imply congruence if the bisecting leads to congruent triangles, but it's not a standalone guarantee of congruence. Option D mentions that the two quadrilaterals have the same area, but equal area does not imply congruence as there can be many non-congruent quadrilaterals with the same area. Therefore, the correct answer for minimal conditions for congruence would be option A: Sides of one quadrilateral being equal in length to the sides of the other quadrilateral is a sufficient condition for congruence.