Firefighters arrived to a fire in the 3200 block of Duke Homestead Road just before 3 a.m., said Deputy Fire Chief Chris Iannuzzi.
Officials said the resident of the home was awakened by the smoke alarm after falling asleep while frying fries on the stove.
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The fire caused heavy damage to the kitchen, attic and roof.
There were no injuries, officials said.
The adult and two children were displaced but are staying with relatives.
Deputy Chief Iannuzzi said unattended cooking is the leading cause of cooking fires in Durham.
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