cathetus theorem - Kathetensatz
Greek - Κάθετος
The “Katheten Satz” (as known in German maths text books) is
$${ a^2 = p \cdot c}$$ , where p is the adjacent segment of the hypotenuse c to the leg a.
$${ b^2 = q \cdot c}$$ , where q is the adjacent segment of the hypotenuse c to the leg b.
These corollaries can be derived using similar triangles in the right-angled triangle.
proof of Pythagoras’ theorem
Adding both corollaries ("Kathetensätze"), you get
$${ a^2 + b^2 = p \cdot c + q \cdot c}$$ $${ a^2 + b^2 = (p + q) \cdot c}$$ $${ a^2 + b^2 = c \cdot c}$$ $${ a^2 + b^2 = c^2}$$
q.e.d.