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近年来,折纸中所蕴含着的丰富数学知识备受各地中考命题者的青睐,设计了许多别具创意的折叠问题,可谓异彩纷呈。现釆撷其中较有代表性的试题,予以例析。一、轴对称性质是解折叠问题的基本原理解折叠问题的关键是抓住折痕的性质:折痕即对称轴,被覆盖部分与折起部分关于折痕成轴对称图形。例1:三角形纸片 ABC中,∠A=65°,∠B=75°。将纸片的一角折叠,使点 C落在△ABC 内(如图1)。若∠1=20°,则∠2的度数是__。(2002年山东省聊城市中考试题)解:在△ABC 中,由∠A=65°,∠B=75°,得
In recent years, the rich mathematics knowledge contained in origami has been favored by the proposition examiners all over the country, and many creative folding problems have been designed. Now that more representative of the test questions, to be exemplified. First, the axisymmetric nature is the basic understanding of the unfolding problem. The key to the folding problem is to grasp the nature of the fold: the crease is the axis of symmetry, and the covered part and the folded part form an axisymmetric pattern about the crease. Example 1: Triangle paper ABC, ∠A=65°, ∠B=75°. Fold the corner of the sheet so that point C falls within △ABC (Figure 1). If ∠1=20°, the degree of ∠2 is __. (2002 Liaocheng test in Shandong Province) Solution: In △ABC, by ∠A=65°, ∠B=75°,