Question 1

$\Delta$ABC中，F、E分別為$\overline{AB}$、$\overline{AC}$的中點，則下列敘述何者錯誤？

Accepted Answer

重心為三個角平分的交點

Answer

重心是G點

Answer

6$\Delta$CGD = $\Delta$ABC

Answer

$\frac{2}{3}$$\overline{AD}$ = $\overline{AG}$

Question 2

$\Delta$ABC中，F、E分別為$\overline{AB}$、$\overline{AC}$的中點，已知$\overline{BG}$ = 24，求$\overline{BE}$ = ？

Accepted Answer

36

Answer

30

Answer

12

Answer

48

Question 3

$\Delta$ABC中，F、E分別為$\overline{AB}$、$\overline{AC}$的中點，已知$\Delta$AFG = 12，求$\Delta$ABC= ？

Accepted Answer

72

Answer

48

Answer

84

Answer

60

Question 4

直角$\Delta$ABC中，$\angle C=90^{\circ}$，中線$\overline{AD}$、$\overline{BE}$相交於G點，若$\overline{AB}$ = 10，$\overline{BC}$ = 6，求四邊形GDCE的面積 = ？

Accepted Answer

16

Answer

20

Answer

24

Answer

12

Question 5

直角$\Delta$ABC中，$\angle C=90^{\circ}$，中線$\overline{AD}$、$\overline{BE}$相交於G點，若$\overline{AB}$ = 30，$\overline{BC}$ = 18，求$\Delta$AGE的面積 = ？

Accepted Answer

36

Answer

24

Answer

30

Answer

42

Question 6

已知直角$\Delta$ABC兩股長$\overline{BC}$ = 3，$\overline{AB}$ = 4，G為$\Delta$ABC的重心，求重心G到$\overline{AC}$的距離為何？

Accepted Answer

$\frac{4}{5}$

Answer

1

Answer

$\frac{2}{3}$

Answer

$\frac{2}{5}$

Question 7

如圖，$\Delta$ABC三中線相交於G點，且$\overline{GA}$ = 20，$\overline{GB}$ = 18，$\overline{GC}$ = 14，求$\overline{AD}$ + $\overline{BE}$ + $\overline{CF}$ = ？

Accepted Answer

78

Answer

72

Answer

28

Answer

60

Question 8

如圖，$\Delta$ABC三中線相交於G點，且$\overline{AD}$ = 30，$\overline{BE}$ = 27，$\overline{CF}$ = 21，求$\overline{GA}$ + $\overline{GB}$ + $\overline{GC}$ = ？

Accepted Answer

52

Answer

72

Answer

60

Answer

54

Question 9

如圖，平行四邊形ABCD對角線相交於F點，E為$\overline{BC}$的中點，$\overline{AE}$交$\overline{BD}$於G，若$\overline{FG}$ = 3，且$\Delta$AGF的面積為8，求$\Delta$CDF的面積 = ？

Accepted Answer

24

Answer

16

Answer

28

Answer

20

Question 10

如圖，平行四邊形ABCD對角線相交於F點，E為$\overline{BC}$的中點，$\overline{AE}$交$\overline{BD}$於G，若$\overline{FG}$ = 3，且$\Delta$AGF的面積為8，求$\overline{BD}$ = ？

Accepted Answer

18

Answer

9

Answer

12

Answer

15

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