That's the one thing about the Purdue OWL and other writing sites: you need to know the name of what you're searching for and know the terminology used by a different site (because some rules have more than one name, especially on different sides of the Atlantic).
Though with Purdue OWL, you can find a
general entry about the use of commas if you type "comma rules" in their search box.
There is indeed such a thing as an
adjective clause, even though the term doesn't pop up on Purdue OWL. They are clauses that serves as adjectives, because they modify a noun in a sentence. So I assume an adjective phrase is a phrase that modifies a noun but doesn't contain a subject-verb combo.
Clauses contain a subject and verb. Phrases can serve as adjectives as well, but they don't contain a subject-verb combo.
Dogs, the animal that is man's best friend, are highly social," would be an example of a sentence containing an adjective clause. The clause modifies dog. We set it off with commas because it doesn't change the core meaning of the sentence.
As I understand it, "Dogs, man's best friend, are highly social animals," contains an adjective phrase as modifier.
"Lying by the fire, the dog slept deeply" is is an adjective phrase that contains a participle. "lying by the fire" isn't considered a clause, because it technically contains no subject. It's a type of phrase called a
participle phrase, because it contains a participle. I assume it is called a phrase and not a clause because it doesn't contain a subject.
But here's what confuses the heck out of me. Because
In the UK, they call the former participle clauses or adverbial clauses (I don't know why they call them adverbial when they serve as adjectives, except they can contain adverbs sometimes).
Relative pronouns can function as subjects, according to some sources. If that is true, then "The dog, who was lying by the fire, slept deeply" would indeed be a participle clause. But I haven't noticed the UK sites distinguishing between participle phrases and clauses either.
It seems to cause some consternation online too. I guess it's not important what one calls something if one uses commas correctly and doesn't dangle or misplace the participle or modifier.
But argh, it gives me a headache, and it makes googling (or asking) questions about usage difficult sometimes.
In any case, to Kendall (the op), you used commas correctly in your examples.
His share of the money, consisting of $100,000, was given to him on Monday.
Would be an adjective phrase (and a participle phrase in US terminology). Except, it could be implied to mean "which consisted of 100,000." Then it would be a participle clause (as the British call it).
I arrived at Lucrezia’s and Kat, a heavy, short, redhead with a pleasant, fun look about her, sat in the waiting area near the front door.
would be an adjective phrase (no subject-verb combo and no relative pronoun).
Finally, sick of him treating her like a maid, she left his house to live in a woman’s shelter.
This is another phrase, because it doesn't contain a subject-verb combo. Except if you worded it: "Mary, who was sick of him treating her like a maid, left to live in a women's shelter," would be considered a clause, because "who" is also a relative pronoun.
I think
I hope this didn't confuse you more, but the whole clause vs phrase thing gives my brain a workout.