In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle.
Let ABC be right-angled at A.
The right angle is at vertex A, so BC is the hypotenuse.
Construct squares on each side.
Draw AL parallel to BD through A.
Join AD, FC. Triangle ABD = triangle FBC.
Square ABFG = rectangle BDLM. Similarly for the other side.
Therefore: square on AB + square on AC = square on BC.