Corresponding Squares Explained
Corresponding squares are an advanced endgame concept that generalises opposition to complex K+P endings where simple opposition and triangulation are insufficient. Each square for one king has a "corresponding" square for the opponent's king, if the opponent can always reach their corresponding square, the position holds.
The concept
In complex K+P endings, pairs of squares are "linked", if White's king reaches square X, Black's king must reach corresponding square Y to maintain the draw (or vice versa). If the defending king cannot reach its corresponding square, the attacker breaks through.
How to find them
Start from the simplest pairs (opposition squares) and work outward. Label squares with numbers, each square gets the same number as its corresponding partner. If both kings are on the same number, the player to move is in zugzwang.
Training
This is an advanced technique. Study annotated K+P endgames in the legends database and solve endgame studies that require corresponding squares analysis.