Question
Prove that the diagonals of a rectangle are perpendicular if and only if the rectangle is a square.
Solution
Let ABCD be the given rectangle.
Take A as origin.
Let
Now,
Take A as origin.
Let
Now,
Also, 
.
Now diagonals AC and BD are perpendicular if
is perpendicular to 
i.e. iff
i.e. iff
i.e. iff
i.e. iff
i.e. iff
i.e. iff
i.e. iff AD = AB
i.e. iff rectangle ABCD is a square.
Hence the result.
.Now diagonals AC and BD are perpendicular if
is perpendicular to i.e. iff
i.e. iff
i.e. iff
i.e. iff
i.e. iff
i.e. iff
i.e. iff AD = AB
i.e. iff rectangle ABCD is a square.
Hence the result.
