First of all, a brief introduction.

At Rt△abC, ∠ ACB = 90, and cd is the height on the hypotenuse AB, then the projective theorem is as follows: CD? ; =AD DB，BC？ =BD BA，AC？ =AD AB .

Second, the projective theorem

Projection Theorem, also known as Euclid Theorem: In a right triangle, the height on the hypotenuse is the median term of the ratio of the projection of two right-angled sides on the hypotenuse, and each right-angled side is the median term of the ratio of the projection of this right-angled side on the hypotenuse to the hypotenuse. Projective theorem is an important theorem in mathematical graphic calculation.

Third, the concept of proof.

1, because the projection is to scale the length of the original figure (called the height in the triangle) and 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). Then this ratio should be the cosine of the angle formed by the plane.

2. 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. This ratio can be proved by calculating it in a triangle on the plane.

Four. Presenter's introduction

1, Euclid (Greek: ε υ κ λ ε ι δ η? 325 BC-265 BC), an ancient Greek mathematician, was called "the father of geometry". During the period of Ptolemy I Soter (323 BC-283 BC), he was active in Alexandria.

2. His most famous book, The Elements of Geometry, is the foundation of European mathematics, which summarizes five postulates of plane geometry and is widely regarded as the most successful textbook in history. Euclid also wrote some works about perspective, conic curve, spherical geometry and number theory.

Verb (abbreviation of verb) expansion

Length projection is one of the important theorems in solid geometry. It is based on the nature of right triangle. As an ancient and subtle branch of geometry, projective geometry originated in17th century.