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文[1]P_(456)总复习题第78题:一三角形的内外角三等分线共十二条,求证:(1)在六条内角三等分线中,与每边相邻的两线各交于一点,这三交点是一正三角形的顶点,(Morley 定理)如图1.(2)在六条外角三等分线中,与每边相邻的两线各交于一点,这三交点也是一正三角形的顶点;如图2.(3)在每一内角的两条三等分线及不相邻外角的四条三等分线中,与每边相邻的两线各交于一点,这三交点也是一正三角形的顶点.如图
Text [1] P_ (456) Overall Review Question 78: The inside and outside corners of a triangle have a total of 12 bisecting lines. Proof: (1) In the six internal angles, the three bisectors, two adjacent to each side The lines intersect at one point. The three intersection points are the vertices of an equilateral triangle. (Morley’s theorem) Figure 1. (2) In the six outer corners and three bisectors, the two adjacent lines on each side intersect at one point. The intersection point is also the vertex of an equilateral triangle; as shown in Figure 2. (3) In each of the three bisectors of the inner corner and the four bisectors of the non-adjacent outer corners, each of the two adjacent lines of each side is intersected. At one point, these three intersection points are also the vertices of a regular triangle.