把空间问题转化为平面问题来研究,是立体几何中的重要思想.本文中的“折”化“直”问题即求线段之和最小值问题,就是充分应用这一思想,根据不同题目及其立体图形的结构特征,发挥空间想象力,把空间问题转化为平面问题来解决.现举例如下:一、对称性的应用例1已知二面角α-l-β的大小为60°,点M、N分别在平面α、β内,点P到平面α、β的距离分别为2和3,则△PMN的周长的最小 The study of transforming the space problem into the plane problem is an important idea in the solid geometry.In this paper, the problem of seeking the minimum value of the line segments is to fully apply this idea, Different topics and the three-dimensional graphics of the structural features, play space imagination, the space problem into a plane problem to solve .Examples are as follows: First, the application of symmetry Example 1 known dihedral angle α-l-β size 60 °, the points M, N are in the plane α, β respectively, the distance from the point P to the plane α, β is 2 and 3 respectively, then the minimum of the circumference of △ PMN