If someone tries to kill you, and fails, are you allowed to kill him back in Islam?
If you're cornered and have no way out but to kill the individual, then this would be considered "self defense" and it is allowed in Islam. But if you're free and you know that no dangerous harm will happen to you any more, but you're still angry and want to revenge, then that wouldn't be allowed in Islam. Let us look at the following Noble Verse:
"If thou dost stretch thy hand against me, to slay me, it is not for me to stretch my hand against thee to slay thee: for I do fear God, the cherisher of the worlds. (The Noble Quran, 5:28)"
I think this Noble Verse perfectly answers the question, and needs no further elaboration.
Back to Islam and Terrorism section.
Does Islam really encourage Muslims to take revenge?
Forgiveness and revenge in Islam. There is a difference between being a peaceful person, and a coward hypocrite in Islam.