Defend against check and avoid pin
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Black just played Qc5+, and White is now in check. White has three legal moves to defend against the check: 1.Qe3? would lose the queen to 1...Qxe3+. 1.Qf2? would allow a pin 1...Bd4!, also losing the queen. Therefore, the only good move is Kh1.
The next example is a bit more complicated:
Black just gave a check with Bb4+.
Note that the White also seems to threaten Nxc7, but it is not a real threat because of Black can counter that with the back-rank mate Ra1#.
Black has four legal moves to defend against the check:
1...Kf6? loses to the intermediate check Bc3+. From c3 the bishop protects a1, and White can capture the knight on the next move.
1...Ke8? would allow 2.Nxc7+ with check, and forking the rook.
1...Kd8? would allow a winning pin with 2.Ba5!.
1...Kd7! is the only correct defence.
In these avoid levels, you have to spot any threats of your opponent before your move, and also after your move. This is good practice so you don't fall in the traps set by your opponent.
If you don't spot the threat, or the line to be avoided, you can always check the solution page, which shows both.