Traditional Culture Encyclopedia - Photography major - Is the projection theorem the content of high school liberal arts?
Is the projection theorem the content of high school liberal arts?
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.
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