三角形ABC与A'B'C'不全等,且不在同一平面内,AB//A'B',B'C'//BC,C'A'//CA.求证AA',BB',CC'相交与一点
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![三角形ABC与A'B'C'不全等,且不在同一平面内,AB//A'B',B'C'//BC,C'A'//CA.求证AA',BB',CC'相交与一点](/uploads/image/z/942030-54-0.jpg?t=%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%8EA%27B%27C%27%E4%B8%8D%E5%85%A8%E7%AD%89%2C%E4%B8%94%E4%B8%8D%E5%9C%A8%E5%90%8C%E4%B8%80%E5%B9%B3%E9%9D%A2%E5%86%85%2CAB%2F%2FA%27B%27%2CB%27C%27%2F%2FBC%2CC%27A%27%2F%2FCA.%E6%B1%82%E8%AF%81AA%27%2CBB%27%2CCC%27%E7%9B%B8%E4%BA%A4%E4%B8%8E%E4%B8%80%E7%82%B9)
三角形ABC与A'B'C'不全等,且不在同一平面内,AB//A'B',B'C'//BC,C'A'//CA.求证AA',BB',CC'相交与一点
三角形ABC与A'B'C'不全等,且不在同一平面内,AB//A'B',B'C'//BC,C'A'//CA.求证AA',BB',CC'相交与一点
三角形ABC与A'B'C'不全等,且不在同一平面内,AB//A'B',B'C'//BC,C'A'//CA.求证AA',BB',CC'相交与一点
三角形ABC与A'B'C'不全等,且不在同一平面内,AB//A'B',B'C'//BC,C'A'//CA.
则平面ABC//平面A'B'C',且△ABC∽△A'B'C'
可知:AB/A'B'=BC/B'C'=AC/A'C'不等于1,设AB>A'B',延长AA'、BB'交于点O,则AB/A'B'=OA/OA'=OB/OB'=BC/B'C'=AC/A'C'
所以,延长CC'也一定可以交于O点,使OA/OA'=OB/OB'=OC/OC'
从而得出:AA',BB',CC'会相交于一点