Which part of Congress must approve a proposed amendment to the Constitution?

No part of congress can amended the Constitution of the United States.

First it takes 2/3's of both houses to 'propose' an amendment to the Constitution or 2/3's of all the 'states' legislators to purpose an amendment (this has not happen yet).

It then takes a 3/4 vote of the 'states' legislators of the United States, which would presently have to be 38 states being that 2/3's is 37.5 states.

Or ratifying conventions in 3/4's of the states approve it, again this would be 38 states. note: This only has happened once, and that was the 21st Amendment, which ended 'prohibition'.

So you see only the States can amend the U.S. Constitution.