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歡迎您訪問數學考題練習:如圖所示,在△ABC中,M是邊AB的中點,N是!

數學考題練習:如圖所示,在△ABC中,M是邊AB的中點,N是

更新時間:2024-01-12 16:25:06作者:貝語網校

如圖所示,在△ABC中,M是邊AB的中點,N是邊AC上的點,且,CM與BN相交于點K,若△BCK的面積等于1,則△ABC的面積等于

A.3

B.

C.4

D.

試題答案

C

試題解析

連接AK,分別求出三角形AKC的面積、三角形AKB的面積與的三角形BKC的面積的比值,求出各自的面積,再求三角形ABC的面積.

解答:連接AK,知=,于是三角形AKC的面積為1.

又因=2,于是三角形AKB的面積為2.

故三角形ABC的面積為1+1+2=4.

故選C.

點評:考查了三角形面積的應用.關鍵掌握同底的三角形面積之比等于對應的高之比.

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