证明:
在FD的延长线上截取DH=FD,连接CH
∵FD=DH,BD=CD,∠BDF=∠CDH
∴⊿BDF≌⊿CDH(SAS)
∴BF=HC,
∠F =∠H
又∵∠AEF=∠CEH
∴⊿AEF∽⊿CEH(AA‘)
∴EA :FA=EC:HC
转化为EA×HC=EC×FA
∴EA×FB=EC×FA【等量代换】
D是三角形ABC的边BC的中点,E是AC边上一点,BA和DE的延长线交于点F.求证:EA*FB=EC*FA
D是三角形ABC的边BC的中点,E是AC边上一点,BA和DE的延长线交于点F.求证:EA*FB=EC*FA
数学人气:977 ℃时间:2020-01-29 22:35:39
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