Very very unlikely. It would be fecal transmitted. You can get roundworms from a cat, which in rare cases results in eye lesions, but tapeworms....eh. You probably don't have to worry. If you have young children worm your cats and dogs often.
Whoops I forgot to say that your vet should be able to either give at the clinic or send home the prescription of Drontal (or whatever broad-spectrum wormer they use) for you to give. And dogs, Heartgard or Iverheart (worming for heartworms) usually worm for other types of worms every month. Luck!
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