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if [[ $a == $b && $b == $c ]]
elif [[ $a == $b || $b == $c || $a == $c ]]
How about now?
Now it's perfect! ;)
It is not necessary.
If a == b, and b == c, that implies that a == c, by Transitive Property of Equality
You are right.
That's why there is no a==c part in the first if-clause.
Here we, however, are talking about the second elif-clause, ISOSCELES, and now, omitting a==c part makes it buggy.