SELECT
(
CASE
WHEN A = B AND B = C THEN 'Equilateral'
WHEN
A = B AND A + B > C OR
A = C AND A + C > B OR
B = C AND B + C > A THEN 'Isosceles'
WHEN A + B > C AND A + C > B AND B + C > A THEN 'Scalene'
ELSE 'Not A Triangle'
END
) AS triangle_type
FROM Triangles;