Question

Diagonals of a rectangle are equal and perpendicular is this statement true? Give reason for your answer.

Answer 1

The diagonals of a rectangle are equal and but not perpendicular hence, the above statement is false.

Proof:-

$AB=CD$ and $AD=BC$

So,

$\begin{array}{cc}A{C}^2& =A{D}^2+C{D}^2\\ & =B{C}^2+A{B}^2\left[AB=CD\right]\\ & =B{C}^2+C{D}^2\left[AD=BC\right]\\ & =B{D}^2\end{array}$

So, $A{C}^2=B{D}^2\Rightarrow AC=BD$

So, the diagonals are equal to each other but we cannot say anything about them being perpendicular.