為什麼在全等三角形的證明中,SSA不是證明條件之一?

2007-05-07 8:32 am
如題。

請不要引用一大段無關痛痕資料,我要的是言簡意賅,而且歡迎大家用圖作回答。

回答 (1)

2007-05-07 11:18 am
✔ 最佳答案
為什麼在全等三角形的證明中,SSA不是證明條件之一?
Consider the following triangles:

圖片參考:http://in.geocities.com/myisland8132/70070507001301.bmp


Here:

side AB is congruent to side DE (S)
side AC is congruent to side DF (S)
angle C is congruent to angle F (A)

But the triangles are not congruent, as you can see.

What happens is this: if you draw a vertical line through point A in
the first triangle, you can sort of "flip" side AB around this line to
get the second triangle. If we were to lay one triangle on top of the
other and draw the vertical line, this is how it'd look.

圖片參考:http://in.geocities.com/myisland8132/70070507001302.bmp



You can see that side DE is just side AB flipped around the line. So
we haven't changed the length of the side, and the other side AC (or
DF) is unchanged, as is angle C (or F). So these two triangles that
have the same SSA information, but they're not congruent.


收錄日期: 2021-04-25 16:55:02
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070507000051KK00130

檢視 Wayback Machine 備份