Basic Endgame: King vs King and Pawn

Hi guys! Welcome to my first blog about Endgame studies! I appreciate it! For my friends who have been reading my previous blog about chess variants, I didn't do part 2 (yet) because I am trying to know how to put Atomic chess traps in the "Insert chess game of diagram" button. I am sorry for the wait. Anyway, in this blog, I will teach you, from white and black's perspectives, on how to win or draw this position. Now let's get started! (A huge thank you for @RohanV7 for coming up this idea!)

Rule of the square

The rule of the square determines whether a queen can promote on the eighth rank, unassisted by the king and are unable to be prevented by the enemy king. Let's look at the position below for an example.

In the diagram above, you can see if the king get get to the highlighted or the square around it, the king can catch the pawn, otherwise the pawn wins the race! Therefore, in that position, if it is black's move, the king can stop the pawn. However, if white moves the pawn first, white wins.

Rook pawn

A pawn on the a-file or h-file have a much lesser chance of promoting. This pawn is called a Rook pawn. The reason the pawn have a lesser chance of promoting is black can always draw if the enemy king get to the square in front of the pawn, which means it can't be driven away. Another way to draw is when his king went to c8, for an a-pawn and reach f8 for an h-pawn. 

if the white king are able to reach the highlighted squares, white's pawn can promote.

Critical squares

A critical square is a square such that if the white king occupies it, the pawn can be forced to promotion regardless where the black king is, assuming black can't capture the pawn. Accurate play is still required even if the king is on the critical square.

Pawns other than Rook pawns

The squares highlighted are the critical squares. As you can see, pawns other than Rook pawns have a very good chance of promoting since there are many critical squares for the king.

Opposition

Opposition means when 2 kings face each other, with 1 square in between, the side with the move may have to move away and let the opposing king advance more. The other king has the opposition.

Example 1

Example 2

Example 3