You can shorten the comparisons that use and by using chained comparisons, and by dropping one of the tests (they are mutually exclusive), using else instead:
if a == b == c:
print('Equilateral triangle')
elif a != b != c != a:
print('Scalene triangle')
else:
print('Isosceles triangle')
Note that Python's if syntax doesn't require any parentheses around the test expressions.
Next, you could look at these values as a set, and test how many elements are in the set:
unique_lengths = len({a, b, c})
if unique_lengths == 1:
print('Equilateral triangle')
elif unique_lengths == 2:
print('Isosceles triangle')
else:
print('Scalene triangle')
This can then be turned into list lookup, mapping 1, 2 and 3 to triangle class names; I slotted None into the 0 position:
classes = [None, 'Equilateral', 'Isosceles', 'Scalene']
print(classes[len({a, b, c})], 'triangle')
if a == b == c