數學平面幾何問題X1

2010-09-17 4:33 am

圖片參考：http://imgcld.yimg.com/8/n/HA00543461/o/701009160110913873371610.jpg

1. In the figure 1, DB=DG ,EC=EF and DG//EF .Find angle BAC.

2.In the figure 2, FA=FD ,BC=BD and FD//EC .Prove that
a) Triangle BFD全等Triangle CEB
b) AF=bE

回答 (1)

用戶2053

2010-09-17 8:39 am

✔ 最佳答案

1)ㄥA + ㄥB + ㄥC = 180° .....(1)因GD // FE , 故ㄥGDE + ㄥFED = 180° .....(2) 又 DB=DG 及 EC=EF , 故ㄥGDE = 2ㄥB 及ㄥFED = 2ㄥC , 代入(2) :2ㄥB + 2ㄥC = 180°ㄥB + ㄥC = 90° , 代入(1) :ㄥA = 90°
2)a)FD // EC 故ㄥBFD = ㄥCEBBD = CDㄥEBC = 180° - ㄥFAD - ㄥBCD因 AF = DF , 故ㄥFAD = ㄥFDA
因BC = BD , 故ㄥBCD = ㄥBDC所以ㄥEBC = 180° - ㄥFDA - ㄥBDC = ㄥFDB△BFD =~= △CEB (A.S.A.)b)AF =[ DF = BE (全等△對應邊) ]

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