读了《中小学数学》初中版2014年第1—2期刊登的《勾股定理的八种面积证法》一文后,觉得作者从众多的的证法中选取出具有代表性,浅显易懂的八种证法,易于学生理解和掌握,值得借鉴.其中证法4(内切圆法)代数变换较难想到,觉得意犹未尽,特作如下补充.如图1,∠ACB=90°,点D,E,F分别为三边CA,AB,BC上的切点.O为内心,将ΔABC补成如图所示 After reading the “Average Area Proof Method of the Pythagorean Theorem” published in the 1st and 2nd editions of the “Primary and Secondary Mathematics” Junior High School Edition in 2014, I felt that the author chose a representative from a wide range of proofs, making it easy to understand. The eight authentication methods are easy for students to understand and master, and are worth learning from. Among them, the authentication method 4 (inscribed circle method) is harder to think of algebraic transformation and it feels like it has not been fully implemented. It is specially supplemented as follows. As shown in Figure 1, ∠ACB=90°, D, E, and F are cut points on the three sides CA, AB, and BC, respectively. O is the heart, and ΔABC is complemented as shown in the figure.