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三边长分别是3、4、5的三角形,我们十分熟悉.把这个简单的三角形进行折叠,做一做就会发现许多有趣的结论.下面就结合三角形的相似与勾股定理、直角三角形的面积等探究折叠这个最简单的直角三角形,计算折痕长度的问题,供参考.1经过短直角边上的某一等分点(距离斜边端点较近)计算折痕长度.例1如图1,已知△ABC中,∠ACB=90°,BC=3,AC=4.D是BC的三等分点,且D距离B点较近,沿着过点D的直线折叠图形,使得点C折叠后落在斜边AB上,计算折痕DE的长度.
Triangular length of the three sides were 3,4,5, we are very familiar with this simple triangle to be folded, do one to do will find many interesting conclusions below the combination of the triangle similarity and the Pythagorean theorem, right triangle Area, etc. Explore the simplest right-angled triangle that is folded, and calculate the length of the crease for reference .1 Calculate the crease length by passing through an equal point on the shorter-right-angled edge (closer to the end of the hypotenuse). 1, known △ ABC, ∠ ACB = 90 °, BC = 3, AC = 4. D is the BC third of the points, and D from the B point closer, along a straight line D over the folding graph, making Point C is folded and falls on the hypotenuse AB to calculate the length of the fold DE.