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勾股定理及其逆定理是直角三角形的重要性质和判定依据,有关这部分内容的中考题型十分丰富．现以近年来各地中考试题为例,谈一下勾股定理及其逆定理的应用．一、由边的关系探索面积关系例侧 (2005年·绵阳)如图1①,分别以Rt△ABC的三边为直径向外作三个半圆,其面积分别用S_1、S_2、S_3表示,则不难证明S_1=S_2+S_3 (1)如图1②,分别以Rt△ABC的三边为边向外作三个正方形,其面积分别用S_1、S_2、S_3表示,那么S_1、S_2、S_3之间有什么关系？(不必证明)
The Pythagorean theorem and its inverse theorem are the important properties of the right-angle triangle and the basis for its determination. The questions in this part of the examination are very rich. Now take the middle school exams in recent years as an example to talk about the application of Pythagorean theorem and its inverse theorem. First, from the side of the relationship between the exploration of the area relationship example side (2005 · Mianyang) as shown in Figure 11, with three sides of Rt △ ABC as the diameter of three semi-circle outside, the area are used S_1, S_2, S_3, respectively, then It is not difficult to prove that S_1 = S_2+S_3 (1) As shown in Fig. 12, the three sides of Rt △ ABC are taken as the edges and three squares are outward, and the areas thereof are represented by S_1, S_2, and S_3 respectively, then the S_1, S_2, and S_3 What is the relationship between? (do not have to prove)