The specific content of the projective theorem

The projection theorem is for right triangles.

The so-called projection is orthographic projection.

Among them, the vertical foot of a perpendicular line drawn from a point to a straight line is called the orthographic projection of this point on this straight line. A line segment between the orthographic projections of two endpoints of a line segment on a straight line is called the orthographic projection of the line segment on the straight line.

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 the triangle BAD is similar to the triangle ACD,

So AD/BD=CD/AD

So (AD)^2=BD·DC