Soooo I was right? I’m not sure why you said no. And activating and awakening are interchangeable in this situation.
You were right in the sense that Madara gave Nagato the rinnegan as a child. The reason why I said no was because you said that Nagato "awakened" the rinnegan "on his own".
You using the word "awakened" (and then on top of that, saying that he did so on his own) would imply that you believed that the rinnegan was Nagato's own eyes, and that he was the natural inheritor of the dojutsu (which he was not). As we know, Madara is the one who "awakened" those eyes.
Nagato simply activated Madara's rinnegan that Madara gave him.
I must respectfully disagree with your notion that "awakened" and "activated" are interchangeable here. In fact, in the actual conversation between Obito and Konan, Obito corrected Konan on this same thing.
When it comes to dojutsu in the Narutoverse, "awakened" is only ever used when the dojutsu is activated for the first time (by the natural user of that dojutsu). Every subsequent activation of the dojutsu is simply activation, not awakening.
Example:
Sasuke awakened the sharingan when he was a kid when Itachi killed the clan.
Whenever adult Sasuke activates his sharingan, that is not him awakening it. He is simply activating it at that point.
It is the same even in the case of a user of a stolen/gifted eye.
Example: When Madara stole Obito's left eye from Kakashi, Madara proceeded to use Obito's mangekyou sharingan in order to get into kamui's dimension.
However, Madara did not awaken Obito's mangekyou sharingan. Obito awakened his mangekyou sharingan. Madara simply activated Obito's mangekyou sharingan while using it for himself.