How is an Icthyosaur a reptile?

I wanted to know based on its fossilized skeleton, how scientists can conclude that and Icthyosaur was a reptile.
Answers:
Reptiles have external ears made of bone; ichthyosaurs of all types have been found with this repitilian bone ear structures that are not present in any other aquatic species. As a matter of fact, this was the clue by which scientists determined that they had not evolved from amphibians.

Furthermore, there is no evidence of a surface area devoted to gills, which would have had to be large to account for some species of icthyosaur. We instead find a large ribcage, deep and long enough to house large lungs, which makes sense in a completely aquatic animal. While some species of fish have lungs, these are, by and large, rare, and live in shallow waters (such as lakes or ponds) or in intermittent rivers. An animal the size of most icthyosaurs would not have survived in such environments (not enough food, and, in some cases, a lack of pressure against the body would've caused suffocation, similar to the problems beached whales find). Fish also do not give live birth, as ichthyosaurs did, fossilized remnants of which have been uncovered in Germany.

Now, one could argue that, even if they aren't fish, they may still be an aquatic mammal. The problem with this is that the fossilized impressiosn caused by the caudal (tail) fins are vertical, not horizontal. This development has never been observed in marine mammals. Also, marine mammals also do not rely on vision; ichthyosaurs not only had large eye sockets, but also bony rings to provide stability to the eye during episodes of high speed. Opthalmosaurus was even named after the size of these eyes.

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reptiles, mammals, fish.. etc.. all have specific bone structures - not in how they look, but inside the bones. for example, bird bones are extremely porous.
in addition skull formation (if they find a skull) gives several clues as to whether an animals is a reptile, mammal.. etc...
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