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。