Rectangles with Equal Bases and Equal Altitudes are Congruent

Theorem
Let $ABCD$ and $EFGH$ be rectangles.

Then $ABCD$ and $EFGH$ are congruent if:
 * the base of $ABCD$ equals the base of $EFGH$
 * the altitude of $ABCD$ equals the altitude of $EFGH$.

Proof
A rectangle is a parallelogram whose vertices are right angles.

Thus the altitudes of $ABCD$ and of $EFGH$ coincide with the sides of $ABCD$ and $EFGH$ which are adjacent to the bases.

The result then follows from Parallelograms are Congruent if Two Adjacent Sides and Included Angle are respectively Equal.