user2652: In other words, after white's move, black king is not in check.  It is now black's move, but any move that black could make results in check.  Is this a checkmate?  Is there a chess term for this situation?

user3093: No, if there are no more moves available to black then it is a stalemate.
If black has other pieces which have moves available to them they must move those pieces.

user3059: It's called a stalemate, which is a draw.

user1751: 
Putting your king in check is not a legal move as you've realized.
Of course, if Black has any OTHER legal moves he can and should play one of them!
If a side TO MOVE does not have ANY legal moves, that would be a stalemate, not a checkmate (which is delivered only by the side making the check)


2652: <p>In other words, after white's move, black king is not in check.  It is now black's move, but any move that black could make results in check.  Is this a checkmate?  Is there a chess term for this situation?</p>
 3093: <p>No, if there are no more moves available to black then it is a stalemate.</p>

<p>If black has other pieces which have moves available to them they must move those pieces.</p>
 3059: <p>It's called a stalemate, which is a draw.</p>
 1751: <ul>
<li>Putting your king in check is not a legal move as you've realized.</li>
<li>Of course, if Black has any OTHER legal moves he can and should play one of them!</li>
<li>If a side <strong>TO MOVE</strong> does not have ANY legal moves, that would be a <strong><a href="http://en.wikipedia.org/wiki/Stalemate">stalemate</strong></a>, not a <strong>checkmate</strong> (which is delivered only by the side making the check)</li>
</ul>
