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The following code works very well.
it contains two nested cases.
outer case is about a, b, c forms a triangle whether or not.
the inner case is about what a types of triangle is it.
select case when (A+B) >C and (A+C) > B and (B+C) > A
then case when A=B and B=C then 'Equilateral' when A=B or B=C or A=c then 'Isosceles' else 'Scalene'
end else 'Not A Triangle' end from triangles;
Thanks for helping me !!! ;)