几何基础（Geometric basis）.doc

几何基础（Geometric basis） For every reader who loves plane geometry: (source: luoqq330501) (I) Euclidean geometry was originally established: Lets say I have 1: I can draw a line at any point to any other point. Public set 2: a finite segment can be extended. Set 3: you can draw a circle at any point and at any distance. Public 4: all right angles are equal to each other. Set 5: intersecting a straight line and two lines in the same plane. If the two angles of one side and the two angles are smaller than two, the two lines intersect each other on this side. (2) the five geometric models (1) equal product transformation model 1. The two triangular areas of equal height are equal 2. The two triangles are of equal height and the area ratio is equal to their base ratio 3. The base of two triangles is the same, and the area ratio is equal to its height (2) common Angle theorem model One of the two triangles has an equal or complementary Angle, and these two triangles are called conformal triangles. The area ratio of a common Angle triangle is equal to the ratio of the product of the two sides of the corresponding Angle (phase or complementary Angle). (3) butterfly theorem model Any quadrilateral with quadrilateral, rectangle, trapezoid, the proportion of the four parts connected to the diagonal is the same (4) similar triangular model Similar triangles: the same shape, but different sizes of triangles The length of all corresponding lines in a similar triangle is proportional, and this ratio is equal to their similarity ratio The area ratio of a similar triangle is equal to the square of their similarity ratio (5) the dovetail theorem, in which D, E, F is the dot of BC, CA, AB, and AD, BE and CF are intersect at the same point O S deltax AOC = S delta BDO: S S delta c: S delta c Delta bank: delta bank: delta bank of S. Delta S (3) (1) a triangle with a common side is called a cop-sided triangle. Coside theorem: set line AB and PQ at point M, S delta PAB/S delta QAB = PM/QM S