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.

$\blacksquare$

Sources

• 1968: M.N. Aref and William Wernick: Problems & Solutions in Euclidean Geometry ... (previous) ... (next): Chapter $1$: Triangles and Polygons: Theorems and Corollaries $1.24$: Corollary