论文部分内容阅读
2010年第5期《数学通报》刊登了白玉娟、郭璋老师给出的1846号问题“在△ABC中,∠A=90°,AB=AC,点D1,D2在AC上,且AD1=CD2,AE1⊥BD1于E1,延长AE1交BC于F1,AE2⊥BD2于E2,延长AE2交BC于F2.求证:∠AD1B+∠AD2B=∠CD1F2+∠CD2F1”的证明1.我们通过对该问题认真探究反思,得到了该问题的一些有意义的结论:一是该问题的多种证法,二是该问题的变形命题,三是该问题的原型命题,四是问题的推广引申.
Issue No. 5 of 2010 Issue No. 466 given by Bai Yujuan and Guo Zhang, "In ABC, ∠A = 90 °, AB = AC, points D1 and D2 are on AC, and AD1 = CD2, AE1⊥BD1 in E1, extending the intersection of AE1 and BC in F1, AE2⊥BD2 in E2, extending the intersection of AE2 and BC in F2. Proof: ∠ AD1B + ∠ AD2B = ∠CD1F2 + ∠CD2F1 The problem is conscientiously explored and reconstructed, and some meaningful conclusions of the question are obtained. First, there are many kinds of evidences of the question. The second is the deformation proposition of the question. The third is the prototype proposition of the question. The fourth is the extension of the issue.