△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F △ABC中,∠ABC=∠ACB,△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F△ABC中,∠ABC=∠ACB,BD的延
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![△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F △ABC中,∠ABC=∠ACB,△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F△ABC中,∠ABC=∠ACB,BD的延](/uploads/image/z/5271922-10-2.jpg?t=%E2%96%B3ABC%E4%B8%AD%2C%E2%88%A0ABC%3D%E2%88%A0ACB%2CBD%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%A4%E5%A4%96%E8%A7%92%E2%88%A0ACM%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E4%BA%8EE.%E7%9B%B4%E7%BA%BFCE%E4%B8%8E%E7%9B%B4%E7%BA%BFAB%E4%BA%A4%E4%BA%8EF+%E2%96%B3ABC%E4%B8%AD%2C%E2%88%A0ABC%3D%E2%88%A0ACB%2C%E2%96%B3ABC%E4%B8%AD%2C%E2%88%A0ABC%3D%E2%88%A0ACB%2CBD%E7%9A%84%E5%BB%B6%E9%95%BF%E7%BA%BF%E4%BA%A4%E5%A4%96%E8%A7%92%E2%88%A0ACM%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E4%BA%8EE.%E7%9B%B4%E7%BA%BFCE%E4%B8%8E%E7%9B%B4%E7%BA%BFAB%E4%BA%A4%E4%BA%8EF%E2%96%B3ABC%E4%B8%AD%2C%E2%88%A0ABC%3D%E2%88%A0ACB%2CBD%E7%9A%84%E5%BB%B6)
△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F △ABC中,∠ABC=∠ACB,△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F△ABC中,∠ABC=∠ACB,BD的延
△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F △ABC中,∠ABC=∠ACB,
△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F
△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F
(1)当∠BAC>90°时,探究∠CDE与∠F的关系;
①如图一,∠ABC=24°,则∠CDE=_____°,∠F=_____°;
②如图二,∠ABC=32°,则∠CDE=_____°,∠F=_____°;
③由上述结果可以猜想当∠ABC的大小发生变化时,∠CDE与∠F之间的数量关系保持不变,这个数量关系用等式表示为___________________________
(2)如图三,当∠BAC<90°时,∠CDE与∠F之间又有怎样的数量关系?写出你的结论并证明.
△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F △ABC中,∠ABC=∠ACB,△ABC中,∠ABC=∠ACB,BD的延长线交外角∠ACM的平分线于E.直线CE与直线AB交于F△ABC中,∠ABC=∠ACB,BD的延
(1)1.因为BD平分∠ABC,∠ABC=∠ACB
所以∠DBC=1/2∠ABC
由三角形外角公式得:∠ADB=∠ADB+∠ACB=3/2∠ABC
由对顶角公式:∠CDE=∠ADB=3/2∠ABC=36
因为∠FCM=∠ABC+∠F 所以∠F=∠FCM-∠ABC
而CE平分∠ACM所以∠FCM=1/2(180-∠ACB)=90-1/2∠ABC
所以∠F=90-1/2∠ABC-∠ABC=90-3/2∠ABC=54
2.同1:∠CDE=3/2∠ABC=48
∠F=90-3/2∠ABC=48
3.由1、2得∠F+∠CDE=90
(2)结论:∠F+∠CDE=90
证明:由三角形外角公式和对顶角公式得:
∠CDE=∠ADB=∠DBC+∠ACB=1/2∠ABC+∠ABC=3/2∠ABC
∠F=∠FCM-∠ABC=1/2(180-∠ACB)-∠ABC=90-3/2∠ABC
所以∠F+∠CDE=90-3/2∠ABC+3/2∠ABC=90
即∠F+∠CDE=90 可得等式成立于∠BAC的大小无关