Traditional Culture Encyclopedia - Photography major - Mathematical photography theorem model
Mathematical photography theorem model
Formula: As shown in the figure, in Rt△ABC, ∠ ABC = 90, and BD is the height on the hypotenuse AC, then the projective theorem is as follows:
( 1)(BD)? = ad DC, ②(AB)? =AD AC,(3)(BC)? =CD CA .
Equal product formula (4)AB×BC=AC×BD (can be proved by "area method" or similar method) (5)(AB)? /(BC)? = Advertisement/CD
Proof of projective theorem of right triangle: (mainly calculated from similarity ratio of triangle)
1. In △BAD and △BCD, ∫ Abd+∠ CBD = 90, and ∠ CBD+∠ C = 90,
Schematic diagram of projective theorem (geometric sketchpad) ∴∠ABD=∠C,
∠∠BDA =∠BDC = 90。
∴△BAD∽△CBD
∴ AD/BD=BD/CD
Namely BD? = AD DC. The rest can be proved in the same way.
The projective theorem is as follows:
AB? =AD AC,BC? =CD CA
Two formulas have been added:
AB? +BC? =(AD AC)+(CD AC) =(AD+CD) AC=AC? .
Pythagoras proof projection
∵AD? =AB? -BD? =AC? -CD? ,
∴2AD? =AB? +AC? -BD? -CD? =BC? -BD? -CD? =(BC+BD)(BC-BD)-CD? =(BC+BD)CD-CD? =(BC+BD-CD)CD=2BD×CD。
So AD? =BD×CD。
Using this conclusion, we can get: AB? =BD? +AD? =BD? +BD×CD=BD×(BD+CD) =BD×BC,
AC? =CD? +AD? =CD? +BD×CD=CD(BD+CD)=CD×CB。
To sum up, the projective theorem is obtained. It can also be proved by the knowledge of triangle area.
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