Proof of pythagorean theorem. (except string diagram)

As shown in figure 1, when Rt△ABC, ∠ ABC = 90, BD is the Qualcomm on the hypotenuse AC. It is proved that triangles are similar and have the following projective theorems: (1) (BD) 2; =AD DC，(2)(AB)2； =AD AC，(3)(BC)2； =CD AC. From formula (2)+(3): (ab) 2; +(BC)2； = AD AC+CD AC =(AD+CD)AC =(AC)2； , figure 1 is (ab) 2; +(BC)2； =(AC)2, which is the conclusion of Pythagorean theorem.