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select
case when NOT(A+B>C AND A+C>B AND B+C>A)
then "Not A Triangle"
when (A=B AND B<>C) OR (A=C AND A<>B) OR (B=C AND B<>A)
then "Isosceles"
when A<>B AND B<>C
then "Scalene"
when A=B AND B=C
then "Equilateral"
end as output
from TRIANGLES
GROUP BY A,B,C;
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Type of Triangle
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select case when NOT(A+B>C AND A+C>B AND B+C>A) then "Not A Triangle" when (A=B AND B<>C) OR (A=C AND A<>B) OR (B=C AND B<>A) then "Isosceles" when A<>B AND B<>C then "Scalene" when A=B AND B=C then "Equilateral" end as output from TRIANGLES GROUP BY A,B,C;