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如图,△ABC中AB=AC,AD是∠BAC的平分线,BM、BN三等分∠ABC,CN的延长线交AB于E,求证EM∥BN 这是一个能够培养学生的思维的广阔性、灵活性等多种思维品质的不可多得的好题。如果教师能够和学生一起深入研究、探讨本题的各种证法将能收到举一反三、触类旁通、事半功倍之效。 1.由面积证法、三角证法诱发出“纯”几何证法(“综合法”)。一个陌生的几何证明题摆在我们面前,常使人感到无从下手。也许,有一个相当筒单的证法,但是在
As shown in the figure, AB=AC in △ABC, AD is the bisector of ∠BAC, BM, and BN are equally divided into ∠ABC, and the extension of CN is transmitted to AB to E. The verification of EM∥BN is a broad way to cultivate students’ thinking. Sexuality, flexibility and many other qualities of thinking are rare good topics. If teachers can study in depth with the students, and explore the various proofs of this topic, they will be able to receive an analogy, comprehend by analogy, and do more with less. 1. The “pure” geometry verification method (“comprehensive method”) is induced by the Area Certificate Method and the Triangle Certificate Method. A strange geometric proof is placed before us, often making people feel unable to start. Maybe, there is a fairly simple proof, but in