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The content of projective theorem

The Projective Theorem of Right Triangle

The formula is shown in the figure. At Rt△ABC, ∠ ABC = 90, and BD is the height on the hypotenuse AC, then there is a projective theorem as follows:

( 1)(bd)^2; = ad DC,

(2)(ab)^2; =AD AC,

(3)(bc)^2; =CD AC .

It is proved that in △BAD and △BCD, ∠ A+∠ C = 90, ∠ DBC+∠ C = 90, ∴∠A=∠DBC and ∠ BDA. = A.D. DC. Everything else is similar. (It can also be proved by Pythagorean theorem)

Note: Pythagorean theorem can also be proved by the above projective theorem. According to formula (2)+(3):

(ab)^2; +(bc)^2; = ad AC+CD AC =(ad+CD)ac=(ac)^2; ,

That is (ab) 2; +(bc)^2; =(ac)^2; .

This is the conclusion of Pythagorean theorem. [Edit this paragraph] The projective theorem of arbitrary triangle.