F.3 math quadrilaterals(急~)

👨🏻‍🏫 學術台數學

[匿名]

2009-04-13 5:28 am

Figure A shows a piece of rectangle paper ABCD.As shown in figure B,when ABCD is folded along EF, vertices A and C coincide.

a)Prove that △AEF is an isosceles triangle.

b)Prove that △ABF ≅△ADE.

http://s567.photobucket.com/albums/ss118/tony1232_photo/?action=view&current=math1111.jpg

更新1:

看不清楚圖可按左上角的 FULL SIZE

回答 (1)

用戶2053

2009-04-13 6:12 am

✔ 最佳答案

a)ㄥEFC=ㄥEFA(floding relation)
ㄥAEF=ㄥEFC(AD//BC)
So ㄥAEF = ㄥEFA ,therefore △AEF ia an isosceles △.
b)ㄥABF = ㄥADE = 90
AF = AE (isos △)
AB = AD(opposite side of rectangle)
So △ABF ≅△ADE (R.H.S.)

2009-04-12 22:19:23 補充：
The prove of b) is based on △ABF and △ADE.

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