Here is the text of Common Article 3, so you can read it for yourself.
NOTE: The words, "not of an international character" (below) mean "not between nations." Typical "terrorist activities" and "anti-terrorist activities" would both be included as "armed conflict not of an international character."
Art. 3. In the case of armed conflict not of an international character occurring in the territory of one of the High Contracting Parties, each Party to the conflict shall be bound to apply, as a minimum, the following provisions:
(1) Persons taking no active part in the hostilities, including members of armed forces who have laid down their arms and those placed hors de combat by sickness, wounds, detention, or any other cause, shall in all circumstances be treated humanely, without any adverse distinction founded on race, colour, religion or faith, sex, birth or wealth, or any other similar criteria.
To this end the following acts are and shall remain prohibited at any time and in any place whatsoever with respect to the above-mentioned persons: (a) violence to life and person, in particular murder of all kinds, mutilation, cruel treatment and torture; (b) taking of hostages; (c) outrages upon personal dignity, in particular humiliating and degrading treatment; (d) the passing of sentences and the carrying out of executions without previous judgment pronounced by a regularly constituted court, affording all the judicial guarantees which are recognized as indispensable by civilized peoples.
The Parties to the conflict should further endeavour to bring into force, by means of special agreements, all or part of the other provisions of the present Convention.
The application of the preceding provisions shall not affect the legal status of the Parties to the conflict.
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Source of text: http://www.globalissuesgroup.com/geneva/convention4.html
And here is a link to Hamdan v. Rumsfeld => http://laws.findlaw.com/us/000/05-184.html
Blessings to you. May God help us all.