Similar triangles's Projective Theorem

The projection theorem (also called Euclid theorem) is commonly known as the mother-child triangle: in a right triangle, the height on the hypotenuse is the proportional average of the projections of two right-angled sides 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.

For example: (premise: ∠BAD+∠DAC=90 degrees, AD⊥BC) In the formula Rt△ABC, ∠ BAC = 90 degrees, and AD is the height on the hypotenuse BC, then the projective theorem is as follows: (1) (AD) 2; = BD dc,(2)(ab)^2； = BD bc,(3)(ac)^2； =CD BC. Equal product formula (4)ABXAC=BCXAD (proof of usable area)

1. Parallel line bisection theorem

If a set of parallel lines cut on a straight line are equal, then the line segments cut on any straight line (intersecting with this set of parallel lines) are also equal.

2. Parallel cutting theorem

Two straight lines intersect a set of parallel lines, which are proportional to the corresponding line segments of this set of parallel wire cuts.

3. Inference of parallel cutting theorem

A straight line parallel to one side of a triangle cuts the other two sides, and the cut triangle is proportional to the corresponding side of the original triangle.