Amud 82a

תוס' ד"ה כדי

In order that they should not tarry three days without Toroh - כדי שלא ילינו ג' ימים בלא תורה

Summary:
We establish the days of reading the תורה on Monday and Thursday, because those were the days (respectively) on which משה descended and ascended הר סיני for the third time

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תוס' ד"ה ודנין

And we judge on Monday and Thursday - 'דנין בב' ובה

Summary:
עזרא instituted that every city should have a sitting בי"ד twice a week, where previously only one (large) city had a sitting בי"ד (every day).

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תוס' ד"ה ושתהא

And that a woman should comb her hair - ושתהא אשה חופפת

Summary:
One only needs to preform חפיפה on the head but not on the rest of the body (except בית קמטיה), but the custom is to wash the entire body.

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