同一法是初等几何証题时常用的一种方法,它是一种间接証法。在这篇文章里,谈谈同一法的逻辑根据,怎样应用同一法,以及用同一法时应注意的几个问题。 (一)同一法的邏辑根据。我们知道,一个正确的命题,它的逆命题可能正确,也可能不正确。例如,“对顶角相等”是正确的,它的逆命题“相等的角都是对顶角”就不正确了。这是为什么呢?这是因为这个命题的前提“对顶角”这概念的外延与结论“相等的角”这个概念的外延不一致。“相等的角”的外延包含了“对顶角”的外延(如图1),反过来,“对顶角”的外延就不包含“相等的角”的外延,因此 The same method is a commonly used method for elementary geometrical proofs. It is an indirect proof. In this article, talk about the logical basis of the same law, how to apply the same method, and several issues that should be noted when using the same method. (a) The logical basis of the same law. We know that a correct proposition, its converse proposition may or may not be correct. For example, “equal to the vertex angle” is correct, and its inverse proposition “Equal angles are all opposite vertices” is incorrect. Why is this? This is because the extension of the concept of “top angle” and the “equivalent angle” of the conclusion of this proposition are inconsistent. The extension of the “equal angle” contains the extension of the “corner angle” (Figure 1). In contrast, the extension of the “corner angle” does not include the extension of the “equivalent angle.”