That's one of my favorite worm sites for pics! It's the one I would have posted.
Yuppers.
Almost always when owners see 'worms' in the dog's feces, it is tapeworm segments. You will rarely see actual worms in the dog's stool unless it is a very heavy infection (female roundworms especially like to travel looking for a mate) or if you have just dewormed and the dead ones come out.
As for treating, you need a worming medicine with the ingredient Praziquantel. Most common wormers are for roundworm and hookworm, and they will not kill tapeworms. If you recently had fleas, this is most likely the flea tapeworm Dipylidium caninum. Dogs get this worm from eating an infected larval flea. Chances are you killed all of the fleas, but the tapeworm just wasn't mature and shedding segments yet, which is why you are only now seeing them. But it can't hurt to treat for fleas again, just in case.
MarcR, your cat probably had one of the Taeniid tapeworms. The intermediate host for those are rodents and rabbits. No fleas necessary.
~Lindsay~
Would that type of worm have smaller segments? I'm pretty sure the segments the cat shed were shorter than 1/2 inch even when extended.