What is the projective theorem? Complete answer, thank you.

Projection theorem of right triangle (also called Euclid theorem): In a right triangle, the height on the hypotenuse is the proportional average of the projections of two right angles on the hypotenuse. Each right angle is the projection of this right angle on the hypotenuse and the proportional average of the hypotenuse.

The formula is shown in the figure. At Rt△ABC, ∠ BAC = 90, and AD is the height on the hypotenuse BC, the projective theorem is as follows:

1.(ad) 2 = BD Special Zone,

2. (AB BC) 2 = BD,

3. (AC) 2 = CD BC.

This is mainly similar to the introduction of triangles. For example, the proof of "(AD) 2 = BD DC:" is as follows:

In △BAD and △ACD, ∠ b = ∠ DAC, ∠ BDA = ∠ ADC = 90, △ bad ∽△ ACD are similar.

So ad/BD = CD/ad,

So (ad) 2 = BD DC。

Note: Pythagorean theorem can also be proved by the above projective theorem, which is obtained by formula (2)+(3).

(AB) 2+(AC) 2 = (BC) 2, which is the conclusion of Pythagorean theorem.