maths! maths! maths!

2009-08-06 9:24 pm

P .31
2. In the figure, prove that AC // ED.
Hint : Let F be a point on CD such that BF //AC.
Figure :
http://www.flickr.com/photos/29635386@N06/3751741724/
(有點看不清的是47度)

3. In the figure, prove that AB // CD.
Hint : Produce CD to touch BF at F.
Figure :
http://www.flickr.com/photos/29635386@N06/3751742020/

4. In the figure, ABC, DEF and MBEN are staright lines.
A] Find x.
B] Is AC parallel to DF? Expain.
Figure :
http://www.flickr.com/photos/29635386@N06/3751741942/

回答 (1)

用戶9112

2009-08-07 7:28 am

✔ 最佳答案

(2) Use interior angles of parallel lines.
Angle CBD = 180 - 121 = 59
Angle CDE = 59 + 74 = 133
Since angle ACD = 47
Angle CDE + Angle ACD = 133 + 47 = 180
Therefore AC // ED
(3) Angle EDF = 180 - 124 = 56
Angle DFB = Angle EDF + Angle DEF (exterior angle of triangle)
Angle DFB = 56 + 29 = 85
Angle DFB + Angle ABE = 85 + 95 = 180
So AB // CD (interior angles of parallel lines)
(4) x = 124 (opposite anlge)
Angle ABE = 180 -124 = 56
If AC is parallel to DF, then Angle ABE = Angle BEF (alternate angle)
This is obviously not ture, so AC is not parallel to DF

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