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立体几何課本已經給出定理1 对于任一三面角,有下列兩性質成立(其中α,β,γ为三面角的三个面角) 因此条件(ⅰ)和条件(ⅱ)是用一組角(α,β,γ)做面角,能構成三面角的必要条件。假如用一組角(100°,10°,15°)做面角,就不能構成三面角,因为它們滿足条件(ⅱ)而不滿足条件(ⅰ)。用一組角(100°,120°,140°)做面角,也不能構成三面角,因为它們滿足条件(ⅰ)而不滿足条件(ⅱ)。但是同时滿足条件(ⅰ)和条件(ⅱ)的三个角,假如(100°,70°,40°),用它們做面角,能否構成三面角?即,条件(ⅰ)和条件(ⅱ)是否为充分的呢?現行立几課本里沒有給出答复。本文目的就在于对此做出結論——建立其充分条件。
The geometry geometry textbook already gives Theorem 1. For any trihedral angle, the following two properties hold (where α, β, γ are the three face angles of the trihedral angle). Therefore condition (i) and condition (ii) are a set of The angles (α, β, γ) are face angles and can form the necessary conditions for trihedral angles. If a set of corners (100°, 10°, 15°) is used as the face angle, trihedral angles cannot be formed because they satisfy condition (ii) and do not satisfy condition (i). With a set of angles (100°, 120°, 140°) for face angles, trihedral angles cannot be formed because they satisfy condition (i) and do not satisfy condition (ii). But at the same time, if the three corners of condition (i) and condition (ii) are satisfied (100°, 70°, 40°), can we use them as face angles to form a trihedral angle? That is, condition (i) and condition ( Ii) Is it sufficient? There is no reply given in the current textbook. The purpose of this paper is to draw conclusions on this - to establish its sufficient conditions.