Given:
ABCD is a parallelogram in which AC=BD.
To prove:
Parallelogram ABCD is a rectangle.
Proof:
In triangles ABC and DBC,
AB=DC (opposite sides of parallelogram)
BC=BC (common side)
AC=BD (given)
But these angles are consecutive interior angles on the same side of transversal BC and AB||DC.
By definition of rectangle, parallelogram ABCD is a rectangle.
Hence the theorem is proved.
