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通过提出和应用方量角概念,把四种结论统一到一种,体现了概念在数学研究中的重大作用。1一个问题的四种不同结论问题:如图1,直线AB与直线CD平行,E是平面上除B、D两点外的任意一点。则∠CDE与∠ABE、∠BED(这三个角均不大于π)之间有什么关系?解:根据点E在平面上的位置,分为下面5种类型讨论。类型1:点E在直线AB的上方。这时分为以下三种情况讨论。(1)如图2所示,E在DB延长线的右侧。
By putting forward and applying the concept of square angle, the four conclusions are unified into one, reflecting the significant role of concepts in mathematical research. 1 A question of four different conclusions: As shown in Figure 1, straight line AB and straight line CD parallel, E is the plane except for B, D two points at any point. Then ∠ CDE and ∠ ABE, ∠ BED (these three angles are not more than π) What is the relationship between? Solution: According to the location of the point E in the plane, divided into the following five types of discussion. Type 1: Point E is above the straight line AB. At this time is divided into the following three situations to discuss. (1) As shown in Figure 2, E is to the right of the DB extension line.