suppose T is a right angle whose sides have a b c. is it possible that each of a b c is an odd integer?
No. There are many possible a,b,c combinations that obey the right angle rule
a^2 + b^2 = c^2
and for which a, b, and c are all integers.
However, if they all ODD integers,
a^2, b^2 and c^2 would also be odd. That is impossible because two odd integers add (or subtract) to make an even.