Is the projection theorem the content of high school liberal arts?

The projection theorem is a projective theorem.

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-angled edge is the median of the projection of this right-angled edge on the hypotenuse and the proportion of the hypotenuse.

formula

As shown in the figure, in rt△abc, ∠ BAC = 90, and ad is the height on the hypotenuse bc, then the projective theorem is as follows:

1.(ad)^2=bd

dc，

2.(ab)^2=bd

BC,

3.(ac)^2=cd

B.C.

This is mainly introduced like a triangle, for example, "(ad) 2 = BD.

The proof of dc is as follows:

exist

△bad and △acd, ∠b=∠dac, ∠ BDA = ∠ ADC = 90, △bad∽ACD are similar.

therefore

ad/bd=cd/ad，

So (ad) 2 = BD.

Direct current

Note: Pythagorean theorem can also be proved by the above projective theorem. By formula (2)+(3)

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