Question

does showing that all four of corresponding sides are congruent prove that two quadrilaterals are congruent. what additional information would be needed in order to prove quadrilaterals congruent.

Answer 1

We can have two rhombus that have the same side length, but they can have different internal angles:

So the answer is NO.

In order to prove that the quadrilaterals are congruent, we also need the information that all corresponding internal angles are also congruent.