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求异面直线间的距离为高中《立体几何》的难点.有关书刊介绍不少方法.本文旨在利用三角形面积射影给出它的求法。为此,先证明下面的命题: 若异面直线a,b所在平面成θ度的二面角α-l-β,且B‖l间的距离为c,则异面直线a,b间的距离d=csioθ (A) 证明:设a∈α b∈β在b上任取一点P,作PM⊥l,PN⊥α,M、N为垂足连结MN,由三垂线定理的逆定理知MN⊥l
Finding the distance between different straight lines is a difficult point in high school “solid geometry”. The relevant books and publications introduce many methods. The purpose of this paper is to use the triangular area projection to give its solution. To this end, we first prove the following propositions: If the planes a and b of the different planes form a dihedral angle α-l-β of θ degrees, and the distance between B and l is c, the lines a and b of the different planes are between Distance d=csioθ (A) Proof: Let a∈α b∈β take any point P on b, for PM⊥l, PN⊥α, M, N for the phonologically linked MN, by the inverse theorem of the triple perpendicular theorem MN⊥l