No - it is possible to have a right angled equilateral triange - however this requires that all three angles are right angles, and isn't possible on a flat surface.
I am sorry, Sagji, but I am not referring to YOUR alarm bells.
In addition, many things that are possible can still cause alarm bells to ring. For example: alarm clocks.
If I had said it wasn't possible, ok, call me Euclid and disabuse me. But I carefully didn't say that... so you should exercise equal care.
Otherwise, it's just non-Euclidean correctness.

- O