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所谓面积法,就是根据平面图形面积(用公式表示)的相等或者不相等,来建立一个等式或者不等式,通过演算、推理,从而达到证明一个数学题(或解出一道数学题)的方法。用面积法可证明平面几何中的某些定理和题目,这种方法在证题和解题的过程中构思别具一格,值得一谈。用面积法解题通常是用这样的三个定理:定理1 同底(等底)或同高(等高)的两个三角形面积之比等于它们对应的高或底之比。定理2 两个三角形若有一角彼此相等或互补,则它们的面积之比等于夹该角的两边乘积之比。
The so-called area method is to establish an equation or inequality based on the equal or unequal area of the area of the plane figure (formula), through calculations and inferences, so as to achieve a method to prove a mathematical problem (or solve a mathematical problem). Using the area method to prove some of the theorems and themes in plane geometry, this method is unique in the process of identifying questions and solving problems, it is worth talking about. Using the area method to solve the problem is usually used three such theorems: Theorem 1 with the bottom (equal bottom) or the same height (contour) of the ratio of the two triangles equal to their corresponding high or bottom ratio. Theorem 2. If two triangles have an angle that is equal or complementary to each other, their area ratio is equal to the ratio of the product of the two sides that sandwich the angle.