Using vector prove that if the diagonals of a parallelogram are equal in length then it is a rectangle.
Given That: Let OACB be the parallelogram and diagonals are equal
To Prove: if diagonals are equal, OACB is a rectangle.
Construction: draw a parallelogram and join the diagonal.
Proof:
Let and, then (parallelogram law)
Since (given)
So,
Hence, OACB is a rectangle.