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What does projection mean in mathematics?
The so-called projection is the orthographic projection.

Among them, the vertical foot from a point to a straight line is called the orthogonal projection of the point on this straight line. The 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 nature of triangles:

Theorem In a right triangle, the height on the hypotenuse is the proportional average of the projections of two right angles on the hypotenuse. Each right-angled edge is the median of the projection of this right-angled edge on the hypotenuse and the proportion of the hypotenuse.