Question

How can I prove that two quadrilaterals are congruent to one another?

Answer 1

Generally, you have to put sides an interior angles of one quadrilateral in correspondence with sides and angle of another and to prove that all corresponding pairs of sides and angles are congruent.

Explanation:

The above follows from the definition of congruence.

Of course, in some specific cases there might be easier solution.

For example, you have compare two rectangles (that is, you you know in advance that both quadrilaterals are rectangles). Then all you have to prove is the congruence of a pair of adjacent sides.

In case of two parallelograms the proper way is to compare a pair of adjacent sides and an angle between them.