直三棱锥(俗称“墙角”)的一个有趣的性质: 已知直三棱锥V—ABC,过V向BC、CA、AB作垂线,垂足分别为D、E、F(如图1)则: ∠DVE+∠EVF+∠FVD=π。在证明这个性质时,我们要用到以下几个命题。命题Ⅰ已知直三棱锥V—ABC,过顶点V向底面ABC作垂线,则垂足H是底面△ABC的垂心。命题Ⅱ△ABC的三条高AD、BE、 An interesting property of straight triangular pyramids (commonly known as “corner corners”): Known as a straight triangular pyramid V-ABC, perpendicular to V, BC, CA, AB for vertical lines, respectively, D, E, F (Figure 1) Then: ∠DVE+∠EVF+∠FVD=π. In proving this nature, we need to use the following propositions. Proposition I is known as a straight triangular pyramid V-ABC, perpendicular to the vertex V ABC for the bottom line, then the foot H is the vertical center of the △ ABC. Proposition II ABC Three high AD, BE,