Traditional Culture Encyclopedia - Photography and portraiture - What is the projective theorem? How to understand?
What is the projective theorem? How to understand?
Simply put? It can be proved by triangle similarity.
In △BAD and △BCD, ∫ Abd+∠ CBD = 90, while ∠ CBD+∠ C = 90.
∴∠ABD=∠C,
∠∠BDA =∠BDC = 90。
∴△BAD∽△CBD
∴ AD/BD=BD/CD
Namely BD? = AD DC. The rest can be proved in the same way [1]
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? . [ 1]
Prove projective theorem with Pythagorean theorem
∵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。
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