Statement
If in a parallelogram, the diagonals are equal and perpendicular, then it is a square.

Given:
ABCD is a parallelogram.
AC=BD and AC ^ BDTo prove:
ABCD is a square.
Proof:
Since the diagonals AC and BD are equal,ABCD is a rectangle - - -(i)
(Diagonal property of rectangle)Since the diagonals are perpendicular to each other.
ABCD is a rhombus.
AB=AD - - -(ii)
With consecutive sides equal. (from ii)
ABCD is a square. (by definition of a square)
Hence the theorem is proved.
