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本刊91年第4期介绍了“母子三角形的性质和应用”,本文就“母子三角形”之间存在的其它重要面积关系再作一介绍。在这里,我们不妨将所有存在于三角形内部的各个小三角形,称为子三角形,而原三角形称为母三角形。一般地,我们有下列重要结论: 命题如图1,在△ABC中,DE∥BC,F为BC边上的任意一点,则有: (1)若记△AOE的面积为S_1,△ABC的面积为S,则S_(△ABE)=S_(△ACD)=S_(四边形ADFE)=(S_1S)~(1/2)
The 4th issue of the journal 91 introduces the “property and application of mother-child triangles”. In this paper, we introduce the other important area relationships existing between “maternal and child triangles”. Here, we may wish to refer to all the small triangles that exist inside the triangle as sub-triangles, while the original triangles are called parent triangles. In general, we have the following important conclusions: The proposition is shown in Figure 1. In △ABC, DE∥BC, F is any point on the BC side, then there are: (1) If the area of △AOE is recorded as S_1, △ABC The area is S, then S_(ΔABE)=S_(ΔACD)=S_(quad ADFE)=(S_1S)~(1/2)