Hello, all,
I was wondering the relationship of the Greek Language to that of the Latin Language. I realize that I could easily Google search this question, but I would prefer to hear back from the members of Omniglot.

While studying Koinē and Classical Greek, I came across a lot of similarities between Greek and Latin. I do realize that Latin has a lot of borrowed words from Greek, but I saw other similarities as well.
For instance, several of the declension endings are very similar to one another.
-α -> -a ( feminine nominative singular)
-ος -> -us (masculine nominative singular)
-αι -> -ae (feminine nominative plural)
-οι -> -ī (masculine nominative plural)
-αν -> -am (feminine accusative singular)
-ον -> -um (masculine accusative singular)
-ῳ -> -ō (masculine dative singular)
et cetera, et cetera.

Also, many central vocabulary words in Latin extremely resemble their Greek counterparts.
For instance, the words "ἐστιν" and "est" both mean the exact same thing, "it is". And the 1st person nominative pronouns are identical ("ἐγω" and "ego").

Please do not think less of me for asking this question.

I won't think less of you.
Latin and Greek are both members of the Indo-European language family. Beyond that, I can't really give you more details because my information is likely to be out of date.

Thanks.
OK, thank you anyways. I remember reading somewhere that they were in completely separate branches of the Indo-European language family, but they are so very similar.

They were spoken in relative proximity to each other, which suggests that they remained in contact longer than other branches. Both are relatively conservative compared to, for instance, Germanic or Armenian. Also, you're comparing earlier stages in the history of each branch. If you compare Modern Greek to one of the Romance languages, you won't find as many similarities.

Have you looked at the similarities between, say, Latin and Lithuanian or Greek and Sanskrit? I suspect you might be struck by those as well.

Greek and Latin represent different IE branches. Greek is pretty much the only major language in the Greek branch. Latin was the source of the Romance subbranch of the Italic branch, which is the only surviving subbranch. Latin was highly influenced by Greek, as the Romans considered Greek the only other language worthy of study.

Thank you to both of you.

I have indeed, thank you. There are a number of surprising similarities.

Ah, OK. Yeah, when I was studying Roman history I believe I read something about that.

Thank you all for your time in answering my rather foolish question.

Nothing "surprising" about it. We know that languages don't emerge from nothing, so it's only to be expected that languages spoken in the same geographical area might be ultimately related. The existence of something like the Indo-European family of languages has been a topic of scholarly discourse for over two hundred years.

Italo Celtic too.