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You could also not write the last condition before 'Not A Triangle' to simplify the Query:
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;
If A = B, it doesn't say anything about C (it is not sure than the triangle is ISOSCELES; in fact, it could be EQUILATERAL if A = C).
Here's my version of the script:
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 AND A !=C OR B = C AND B!=A OR A = C AND A!=B THEN 'Isosceles'
END ELSE 'Not A Triangle'
END FROM TRIANGLES;
Hope you enjoy it, fellas!!