The content of the theorem is that 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.

1, the projection is to scale the length of the original figure (called the height in the 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).

2. This ratio should be the cosine of the angle formed by the plane. Make a right-angled triangle on two planes so that the hypotenuse and right-angled edge are perpendicular to the edge (that is, the intersection of the plane where the original polygon is located and the projection plane), then the hypotenuse and the other right-angled edge of the triangle are the length ratio of its polygon, that is, the area ratio of the plane polygon.

3. Make a vertical line from a point to a straight line or a plane, and the vertical foot is the projection of this point. The projection line of each point on a line segment is the projection of this line segment.