[This is an inversion for à la bouteille même. Boire à même is not usually used of cups or glasses, but of bottles, jugs, streams, etc. For it implies that the containing vessel itself is being used to drink out of, and not any smaller vessel. Thus boire à même le verre would suggest that a spoon or smaller receptacle was not used.]
Il est à même de vous comprendre = He is able to understand you.
Cela revient au même = That comes to the same thing.
C’est cela même = That is the very thing.
Faites de même = Do the same.
Ménage
Ils font bon ménage = They live happily together.
Elle fait le ménage = She is doing her housework.
Ménager
*Qui veut voyager loin ménage sa monture = Who wishes to go far spares his horse; He who wishes to live long avoids excess.