配套习题- 巧用中线解决面积问题 -【青果学院】

1/5单选题

难度：

1.

已知P是△ABC内一点，连接PA、PB、PC，把△ABC的面积三等分，则P点一定是（）

A	△ABC的三边的中垂线的交点
B	△ABC的三条内角平分线的交点
C	△ABC的三条高的交点
D	△ABC的三条中线的交点

正确答案：RA==

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

2/5单选题

难度：

2.

AD是△ABC的中线，AB=6cm，AC=4cm，则△ABD和△ACD的周长差为（）

A	6cm
B	4cm
C	2cm
D	无法确定

正确答案：Qw==

PHAgYWxpZ249ImxlZnQiPuino++8muKItUFE5piv4pazQUJD55qE5Lit57q/77yMPGJyPuKItOKWs0FCROWSjOKWs0FDROeahOWRqOmVv+W3rj3vvIhBQitBRCtCRO+8iS3vvIhBQytBRCtDRO+8iT1BQi1BQ++8jDxicj7iiLVBQj02Y23vvIxBQz00Y23vvIw8YnI+4oi04pazQUJE5ZKM4pazQUNE55qE5ZGo6ZW/5beuPTYtND0yY23vvI48YnI+5pWF6YCJQ++8jjxicj48L3A+

3/5单选题

难度：

3.

如图，已知△ABC中，AD是BC边上的中线，有以下结论：①AD平分∠BAC；②△ABD的周长-△ACD的周长=AB-AC；③BC=2AD；④△ABD的面积是△ABC面积的一半．其中正确的是（）

A	①②④
B	②③④
C	②④
D	③④

正确答案：Qw==

PHAgYWxpZ249ImxlZnQiPuino++8muKItUFE5pivQkPovrnkuIrnmoTkuK3nur/vvIw8YnI+4oi0QkQ9Q0Q9PHNwYW4gY2xhc3M9Im1hdGhxdWlsbC1yZW5kZXJlZC1tYXRoIiBzdHlsZT0iZm9udC1zaXplOjIwcHg7Ij48c3BhbiBjbGFzcz0idGV4dGFyZWEiPjx0ZXh0YXJlYSBkYXRhLWNrZS1lZGl0YWJsZT0iMSIgY29udGVudGVkaXRhYmxlPSJmYWxzZSI+PC90ZXh0YXJlYT48L3NwYW4+PHNwYW4gY2xhc3M9ImZyYWN0aW9uIG5vbi1sZWFmIiBtYXRocXVpbGwtY29tbWFuZC1pZD0iNCI+PHNwYW4gY2xhc3M9Im51bWVyYXRvciIgbWF0aHF1aWxsLWJsb2NrLWlkPSI1Ij48c3BhbiBtYXRocXVpbGwtY29tbWFuZC1pZD0iOCI+MTwvc3Bhbj48L3NwYW4+PHNwYW4gY2xhc3M9ImRlbm9taW5hdG9yIiBtYXRocXVpbGwtYmxvY2staWQ9IjYiPjxzcGFuIG1hdGhxdWlsbC1jb21tYW5kLWlkPSI5Ij4yPC9zcGFuPjwvc3Bhbj48c3BhbiBzdHlsZT0iZGlzcGxheTppbmxpbmUtYmxvY2s7d2lkdGg6MCI+IDwvc3Bhbj48L3NwYW4+PC9zcGFuPjxzcGFuPjwvc3Bhbj48c3BhbiBjbGFzcz0ibWF0aHF1aWxsLXJlbmRlcmVkLW1hdGgiIHN0eWxlPSJmb250LXNpemU6MjBweDsiPjxzcGFuIGNsYXNzPSJ0ZXh0YXJlYSI+PC9zcGFuPjwvc3Bhbj5CQzxicj48L3A+PHAgYWxpZ249ImxlZnQiPuKRoOWPquaciUFCPUFD5pe277yMQUTlubPliIbiiKBCQUPvvIzmlYXmnKzlsI/popjplJnor6/vvJs8YnI+4pGh4pazQUJE55qE5ZGo6ZW/LeKWs0FDROeahOWRqOmVvz3vvIhBQitBRCtCQ++8iS3vvIhBQytBRCtDRO+8iT1BQi1BQ++8jOaVheacrOWwj+mimOato+ehru+8mzxicj7ikaLlj6rmnIniiKBCQUM9OTDCsOaXtu+8jEJDPTJBRO+8jOaVheacrOWwj+mimOmUmeivr++8mzxicj7ikaPorr7ngrlB5YiwQkPnmoTot53nprvkuLpo77yM5YiZ4pazQUJE55qE6Z2iPTxzcGFuIGNsYXNzPSJtYXRocXVpbGwtcmVuZGVyZWQtbWF0aCIgc3R5bGU9ImZvbnQtc2l6ZToyMHB4OyI+PHNwYW4gY2xhc3M9InRleHRhcmVhIj48dGV4dGFyZWEgZGF0YS1ja2UtZWRpdGFibGU9IjEiIGNvbnRlbnRlZGl0YWJsZT0iZmFsc2UiPjwvdGV4dGFyZWE+PC9zcGFuPjxzcGFuIGNsYXNzPSJmcmFjdGlvbiBub24tbGVhZiIgbWF0aHF1aWxsLWNvbW1hbmQtaWQ9IjQiPjxzcGFuIGNsYXNzPSJudW1lcmF0b3IiIG1hdGhxdWlsbC1ibG9jay1pZD0iNSI+PHNwYW4gbWF0aHF1aWxsLWNvbW1hbmQtaWQ9IjgiPjE8L3NwYW4+PC9zcGFuPjxzcGFuIGNsYXNzPSJkZW5vbWluYXRvciIgbWF0aHF1aWxsLWJsb2NrLWlkPSI2Ij48c3BhbiBtYXRocXVpbGwtY29tbWFuZC1pZD0iOSI+Mjwvc3Bhbj48L3NwYW4+PHNwYW4gc3R5bGU9ImRpc3BsYXk6aW5saW5lLWJsb2NrO3dpZHRoOjAiPiA8L3NwYW4+PC9zcGFuPjwvc3Bhbj48c3Bhbj48L3NwYW4+QkTCt2jvvIzilrNBQkPpnaLnp689PHNwYW4gY2xhc3M9Im1hdGhxdWlsbC1yZW5kZXJlZC1tYXRoIiBzdHlsZT0iZm9udC1zaXplOjIwcHg7Ij48c3BhbiBjbGFzcz0idGV4dGFyZWEiPjx0ZXh0YXJlYSBkYXRhLWNrZS1lZGl0YWJsZT0iMSIgY29udGVudGVkaXRhYmxlPSJmYWxzZSI+PC90ZXh0YXJlYT48L3NwYW4+PHNwYW4gY2xhc3M9ImZyYWN0aW9uIG5vbi1sZWFmIiBtYXRocXVpbGwtY29tbWFuZC1pZD0iNCI+PHNwYW4gY2xhc3M9Im51bWVyYXRvciIgbWF0aHF1aWxsLWJsb2NrLWlkPSI1Ij48c3BhbiBtYXRocXVpbGwtY29tbWFuZC1pZD0iOCI+MTwvc3Bhbj48L3NwYW4+PHNwYW4gY2xhc3M9ImRlbm9taW5hdG9yIiBtYXRocXVpbGwtYmxvY2staWQ9IjYiPjxzcGFuIG1hdGhxdWlsbC1jb21tYW5kLWlkPSI5Ij4yPC9zcGFuPjwvc3Bhbj48c3BhbiBzdHlsZT0iZGlzcGxheTppbmxpbmUtYmxvY2s7d2lkdGg6MCI+IDwvc3Bhbj48L3NwYW4+PC9zcGFuPkJDwrdoPGJyPjwvcD48cD7miYDku6XvvIzilrNBQkTnmoTpnaLnp6/mmK/ilrNBQkPpnaLnp6/nmoTkuIDljYrvvIzmlYXmnKzlsI/popjmraPnoa7vvJs8YnI+57u85LiK5omA6L+w77yM5q2j56Gu55qE5piv4pGh4pGj77yOPGJyPjxicj48L3A+

4/5单选题

难度：

4.

如图所示，AD和BE是△ABC的两条中线，相交于点O，设△AOB和四边形CDOE的面积分别为S₁、S₂，则S₁和S₂的关系为（）

A	S₂＞S₁
B	S₂＜S₁
C	S₂=S₁
D	以上答案都不对

正确答案：Qw==

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

5/5单选题

难度：

5.

如图，在△ABC中，D为AC边的中点，E为BD中点，F为CE中点，若△ABD的面积为4，则△BFC的面积为（）

青果学院

A	2
B	1
C	1.5
D	0.5

正确答案：Qg==

PHA+6Kej77ya5LiJ6KeS5b2i5bqV6L655Lit54K55bmz5YiG5LiJ6KeS5b2i6Z2i56ev55+l77yaUzxzdWI+4pazQUJEPC9zdWI+PVM8c3ViPuKWs0JDRDwvc3ViPu+8jFM8c3ViPuKWs0RDRTwvc3ViPj1TPHN1Yj7ilrNCQ0U8L3N1Yj7vvIxTPHN1Yj7ilrNCRUY8L3N1Yj49UzxzdWI+4pazQkNGPC9zdWI+77yMPGJyPuWPiFM8c3ViPuKWs0FCRDwvc3ViPj0077yM6K6+UzxzdWI+4pazQkNGPC9zdWI+5Li6eO+8jCZuYnNwOzxicj7liJnmnIl4K3grMng9NO+8jDxicj7op6PlvpfvvJp4PTE8YnI+5Y2zUzxzdWI+4pazQkNGPC9zdWI+PTE8YnI+5pWF6YCJQjwvcD4=