What is the formula of the projective theorem?

The formula of the projective theorem is as follows:

BD？ = Advertising CD

AB？ = exchange advertising

BC? =CD AC

Projection is to scale the length of the original figure (called height in triangle), so the width is unchanged, and because the area ratio of the plane polygon = the product ratio of the side length. So it is the ratio of the length of the figure (called the height in the triangle).

In a right triangle, the height on the hypotenuse is the proportional average of the projections of two right angles on the hypotenuse, and each right angle is the proportional average of the projections of this right angle on the hypotenuse and hypotenuse.

Formula derivation process:

①∫CD？ +AD？ =AC？ ，CD？ +BD？ =BC？

∴2CD？ +AD？ +BD？ =AC？ +BC？

∴2CD？ =AB？ -Advertising? -BD？

∴2CD？ =(AD+BD)？ -Advertising? -BD？

∴2CD？ =AD？ +2AD BD+BD？ -Advertising? -BD？

∴2CD？ =2AD BD

∴CD？ =AD BD

②∵CD？ = ad BD (certification)

∴CD？ +AD？ =AD BD+AD？

∴AC？ =AD (BD+AD)

∴AC？ =AD AB

③ BC? =CD？ +BD？

BC? =AD BD+BD？

BC? =(AD+BD) BD

BC? =AB BD

∴BC？ =AB BD