【問題】一題圖形證明

[lionhard 10]

已知一直線L ，AB垂直L，CD 垂直L BD中點是M 求證MA=MC 圖位置大概如下^^ 麻煩各位了~~(D在C的正上方，圖弄不好)

D

M

A---------------------------C

B

[keith_291 10]

我猜你要畫的應該是這樣.....

..............B.....................................................................

..............!\....................................................................

..............!..\....................................................................

..............!....\...M...C.....................................................

--------------!------\- -----!-------------------------------------------------------

.............A.......\......!......................................................

........................\....!.....................................................

..........................\..!.....................................................

............................\!.......................................................

.............................D.......................................................

因為M是BD中點

故BM=MD

又角BAM=角DCM=90度

故三角形BAM全等於三角形DCM(RHS)

得AM=MC

[lionhard 10]

可是如果BD中點M不在直線AC上怎辦

[Xiang 10]

圖：

大概說一下就好 BM=DM

所以A'BM和C'DM全等

可推得三角形AMC為等腰三角形

AM=CM

[lionhard 10]

謝謝~