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    -- FIRST CHECK FOR TRIANGLES SELECT CASE WHEN A + B > C AND B + C > A AND A + C > B 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 AS TYPE_TRIANGLES FROM TRIANGLES ;

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    SELECT CASE WHEN A + B <= C OR A + C <= B OR B + C <= A THEN 'Not A Triangle' WHEN A = B AND B = C THEN 'Equilateral' WHEN A = B OR B = C OR A = C THEN 'Isosceles' ELSE 'Scalene' END AS TriangleType FROM TRIANGLES;

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    SELECT 
        CASE 
            WHEN  A = B AND B = C AND A = C THEN 'Equilateral'
            WHEN A + B > C AND A = B OR B = C OR A = C THEN 'Isosceles'
            WHEN A + B > C AND A <> B AND B <> C AND A <> C THEN 'Scalene'
            ELSE 'Not A Triangle'
        END
    FROM TRIANGLES;
    
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    SELECT CASE WHEN A + B <= C OR B + C <= A OR A + C <= B THEN 'Not A Triangle' WHEN A = B AND B = C THEN 'Equilateral' WHEN A <> B AND A <> C AND B <> C THEN 'Scalene' ELSE 'Isosceles' END FROM TRIANGLES

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    Maybe there is a better solution to find the "Not A Triangle" option, but that's what I've found:


    SELECT
        CASE
            WHEN A + B <= C OR B + C <= A OR A + C <= B THEN 'Not A Triangle'
            WHEN A = B AND B = C THEN 'Equilateral'
            WHEN A <> B AND A <> C AND B <> C THEN 'Scalene'
            ELSE 'Isosceles'
        END
    FROM TRIANGLES