The birds were shot at Norton Mills lake in North Stainley, which could have put people's lives at risk as well.
Police say the eight geese and swans were shot and left to die.
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James Arthur, Little Mix and The 1975 are representing the North East region at the Brit Awards 2017.
The terrier was found buried with a nail through its skull in woods in Cleveland last October. Two men have admitted their part in it.
Police are appealing for information following two knife-point robberies in Thornaby.