數學思考題一條

圖片參考：http://imgcld.yimg.com/8/n/HA04628698/o/701104300138913873432490.jpg


a)

ad // bc

△a f d and △a b d with the same base ad and their height are the same.

So the area of them are the same

△a f d = △a b d
△a e d + △a b e = △a e d + △e f d
△a b e = △e f d

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New Farm A = Farm A + △abe - △efd = Farm A

New Farm B = Farm B + △efd - △abe = Farm B

So New Farm A = New Farm B

That means b d is a bisection line of the whole farm.


b)

Step 1 : Drawing the line ad .

Step 2 : Drawing the line bc passing through the point f such that bc // ad ,

Step 3 : Join bd , then bd is the required new boundary.