Even Perfect Number is Triangular

Theorem
All perfect numbers which are even are triangular.

Proof
Let $a$ be an even perfect number.

From the Theorem of Even Perfect Numbers, $a$ is in the form $2^{p - 1} \left({2^p - 1}\right)$ where $2^p - 1$ is prime.

Thus:

The result follows from Closed Form for Triangular Numbers.