在四边形ABCD中,点C'是对角线AC延长线上一点,且AC:CC'=3:2,过点C'作B'C'//BC,C'D'//CD,分别与AB,AD的延长线交于点B',D'.求证四边形ABCD相似于A'B'C'D'
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![在四边形ABCD中,点C'是对角线AC延长线上一点,且AC:CC'=3:2,过点C'作B'C'//BC,C'D'//CD,分别与AB,AD的延长线交于点B',D'.求证四边形ABCD相似于A'B'C'D'](/uploads/image/z/7138696-40-6.jpg?t=%E5%9C%A8%E5%9B%9B%E8%BE%B9%E5%BD%A2ABCD%E4%B8%AD%2C%E7%82%B9C%27%E6%98%AF%E5%AF%B9%E8%A7%92%E7%BA%BFAC%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E4%B8%94AC%3ACC%27%3D3%3A2%2C%E8%BF%87%E7%82%B9C%27%E4%BD%9CB%27C%27%2F%2FBC%2CC%27D%27%2F%2FCD%2C%E5%88%86%E5%88%AB%E4%B8%8EAB%2CAD%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%A4%E4%BA%8E%E7%82%B9B%27%2CD%27.%E6%B1%82%E8%AF%81%E5%9B%9B%E8%BE%B9%E5%BD%A2ABCD%E7%9B%B8%E4%BC%BC%E4%BA%8EA%27B%27C%27D%27)
在四边形ABCD中,点C'是对角线AC延长线上一点,且AC:CC'=3:2,过点C'作B'C'//BC,C'D'//CD,分别与AB,AD的延长线交于点B',D'.求证四边形ABCD相似于A'B'C'D'
在四边形ABCD中,点C'是对角线AC延长线上一点,且AC:CC'=3:2,过点C'作B'C'//BC,C'D'//CD,分别与AB,AD的延长线交于点B',D'.求证四边形ABCD相似于A'B'C'D'
在四边形ABCD中,点C'是对角线AC延长线上一点,且AC:CC'=3:2,过点C'作B'C'//BC,C'D'//CD,分别与AB,AD的延长线交于点B',D'.求证四边形ABCD相似于A'B'C'D'
四个角分别相等,这没问题是吧,根据相似三角形得出对应边比例都为3:2,那么就可以判定四边形想相似了
证明:依题意画出示意图,
∵B'C'//BC,∴ΔABC∽AB'C',则∠ABC=∠AB'C',∠ACB=∠AC'B'且AB/A'B'=BC/B'C'=AC/A'C';
∵C'D'//CD,∴ΔADC∽AD'C',则∠ADC=∠AD'C',∠ACD=∠AC'D'且AD/A'D'=DC/D'C'=AC/A'C';
∴∠ACB+∠ACD=∠AC'B'+∠AC'D',即∠BCD∠...
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证明:依题意画出示意图,
∵B'C'//BC,∴ΔABC∽AB'C',则∠ABC=∠AB'C',∠ACB=∠AC'B'且AB/A'B'=BC/B'C'=AC/A'C';
∵C'D'//CD,∴ΔADC∽AD'C',则∠ADC=∠AD'C',∠ACD=∠AC'D'且AD/A'D'=DC/D'C'=AC/A'C';
∴∠ACB+∠ACD=∠AC'B'+∠AC'D',即∠BCD∠B'C'D',
AB/A'B'=BC/B'C'=AD/A'D'=DC/D'C',
∵∠BAD=∠B'AD',
∴四边形ABCD与四边形AB'C'D'的所有对应角相等,所有对应边成比例,
∴四边形ABCD∽四边形AB'C'D'。
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