How to prove photography theorem

In right triangles A, B, C, the angle C is a right angle. If CD is perpendicular to AB, then the square of CD equals AD times BD AC equals AB times AD BC equals AB times DB. For a right-angled triangle, if A, B and C are used to represent the vertices of the triangle, where A is the right-angled vertex, and the intersection point of the vertical line with point A as the hypotenuse BC at the vertical foot is D, then there is AD 2 = BD * CD. (AD is the middle term in the proportion of BD CD). So, this is one of the properties of right triangle. The proof of this theorem is as follows: ∵ AC ⊥ BD, ∴∠ACD = 90；; ∴∠d+∠dac= 180-90 = 90； ∫∠bad = 90，∴∠bac+∠cad=90； ∴∠bac=∠d； ∠∠ACB =∠ACD = 90，∴△ACD∽△BCA； ∴cd/ac=ac/bc ac^2=bc×cd； ①∠∠d =∠BAC，∠ACD=∠BAD=90，∴△acd∽△bad； ∴bd/ad=ad/cd ad^2=cd×bd； ② ∵△ACD∽△BCA，△ACD∽△BAD，∴△bca∽△bad； ∴ BD/AB = AB/BCAB 2 = BC× BD。 ③ ① ② ③ is a photographic theorem, which can be abbreviated as "the wall grass falls on both sides" and "lie down first, then climb forward".