Question

If I have two parallelograms and all the corresponding sides are equal can I say that they are congruent?

If so, would I be able to write the reasoning as SSSS?

Answer 1

No, not necessarily.

Explanation:

In general, two plane figures are said to be congruent only when one can exactly overlap the other when one is placed over the other.

All four corresponding sides of two parallelograms are equal in length that does mean that they are necessarily congruent because one parallelogram may or may not overlap the other in this case because their corresponding interior angles may or may not be equal.

Two parallelograms will be congruent only when all four corresponding sides are equal in length & one corresponding internal angle is equal.

Answer 2

No

Explanation:

All the sides and all the angles must be the same to be congruent.

For a triangle if the sides are the same then the angles must also be the same (congruent).

For a square all the angles are 90 degrees so if the sides are the same they are congruent.

But for 2 parallelograms, if the corresponding sides are the same the angles may not be, so not necessarily congruent.