Proof 1

Version 3)

🌓 The square of sides a and b are divided as shown in the picture.
🌗 They are then rearranged to fit into the square of c. (This can also be done the other way around)

Version 1)

👹 Consists of a square with sides of a + b
👽 The square contains 4 identical right-angled triangles.

Version 2)

💀 Large square (with an area of c squared) made of 4 right-angled triangles, fitted around a small central square.

Proof by rearrangement