Prosecutors in an activist’s trial presented a home video of his wife belly-dancing as evidence against him on Wednesday. The activist, the prominent blogger Alaa Abdel-Fattah, is being retried in Cairo on charges of protesting and beating a police officer after being sentenced this summer to 15 years in prison. The clip of his wife dancing, clearly at a private family event, prompted Mr. Abdel-Fattah, held in a double-glazed glass cage, to scream, “This is family stuff!” Taher Abul-Nasr, the lead defense lawyer, told the court the video was taken from a computer seized from the couple’s home without a search warrant and called the material irrelevant and defamatory. Most of the evidence presented Wednesday consisted of television images showing various protests and the police chasing civilians, although no scenes of Mr. Abdel-Fattah or any other defendant in the case were shown.