Related properties and formulas of the projection theorem

From the similar properties of triangles, we can get the projection theorem (also called Euclid's theorem), that is, in a right triangle, the height of the hypotenuse is the ratio of the projection of the two right sides on the hypotenuse. item. Each right-angled side is the median of the ratio between the projection of the right-angled side on the hypotenuse and the hypotenuse.

Formula: For the right angle △ABC, ∠BAC=90 degrees, AD is the height of the hypotenuse BC,

Projection theorem,

(AD)^ 2=BD·DC

(AB)^2=BD·BC

(AC)^2=CD·BC

This is mainly due to similar triangles For example, (AD)^2=BD·DC:

It can be seen from the figure that triangle BAD is similar to triangle ACD,

So AD/BD=CD/AD

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So (AD)^2=BD·DC