Checkmate patterns
The opera mate
A rook mates on the back rank while a bishop, from far away, covers the square the king would run to. It is named after Morphy's game at the Paris opera in 1858, which ends with exactly this picture and is the most reproduced finish in chess.
How to spot it
The pattern is a king that has not castled, sitting on e8 or e1 behind a knight or bishop, with the d-file open for your rook and a long diagonal for your bishop. When you have both lines, the sacrifices that clear the file are usually sound.
The positions
Easiest first. Every one is from a real game, and the rating under each board is what it costs the players who have tried it on lichess.
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1. White to play Play it out →Answer
23.Rd8+ Bxd8 24.Re8#
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2. White to play Play it out →Answer
12.Qe8+ Nxe8 13.Rxe8#
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3. White to play Play it out →Answer
29.Qg8+ Rxg8 30.Rxg8#
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4. White to play Play it out →Answer
27.Rd8+ Bf8 28.Rxf8+ Ng8 29.Rxg8#
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5. White to play Play it out →Answer
40.Bf6+ Kg6 41.Rg8+ Kf5 42.Rxg5#
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6. Black to play Play it out →Answer
30...Qxh3+ 31.Kxh3 Rh6+ 32.Bh5 Rxh5+ 33.Qh4 Rxh4#
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7. White to play Play it out →Answer
32.Qxh6+ Bxh6 33.Rh7#
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8. White to play Play it out →Answer
20.Nxe7+ Rxe7 21.Rf8#
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9. White to play Play it out →Answer
29.Bxf6+ Kf7 30.Re7+ Kg8 31.Rg7#
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10. White to play Play it out →Answer
19.Bxf7+ Kxf7 20.Re7+ Kg8 21.f7+ Rxf7 22.Re8+ Rf8 23.Rfxf8#
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11. White to play Play it out →Answer
29.Qh8+ Kxh8 30.Rxh5+ Kg8 31.Rh8#
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12. Black to play Play it out →Answer
36...Rg2+ 37.Bxg2 Rxe1+ 38.Bf1 Rxf1#
Reading about a pattern is the easy half. Motify finds the positions where you missed one, by running your own lichess and Chess.com games through Stockfish, and puts each of them behind two or three puzzles on the same idea so you meet it having just found it three times. See how Motify works.
Positions from the lichess puzzle database, released under CC0.