The answers given by two people upstairs are also correct in a similar way. I just want to add that it is a waste of time to do so in exams (such as the senior high school entrance examination), and 2) teachers may not give full marks. Because, after your "proof", another theorem appeared in mathematics: "If you cross the vertex (right angle) of a right triangle and make a vertical line with the hypotenuse (or the height on the hypotenuse), the two sides will be divided into two proportional line segments, and this vertical line is the proportional average". Like this question. CD is the height on the side of AB, and the dividing side is a double-scale line segment with AD=8 and BD=2, so CD? =AD*BD=8*2= 16

So CD = 4

After the exam, I will write this question:

According to the question: CD? =AD*BD

What is "proportional average"? It is the two "middle" items in the proportional formula. For example, this question AD:CD=CD:BD, CD is an item in the proportion, and CD? =AD*BD .