Can anyone explain the following:

A)

$\displaystyle \frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}$

and the ratio/proportion:

B)

$\displaystyle 1$ : $\displaystyle \frac{1}{\sqrt{2}}$ = $\displaystyle \sqrt{2}$ : $\displaystyle 1$

thanks in advance

How on earth is A) true?