Rectangles with Equal Bases and Equal Altitudes are Congruent
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Theorem
Let $ABCD$ and $EFGH$ be rectangles.
Then $ABCD$ and $EFGH$ are congruent if:
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