初二全等三角形两道题速速速速速速速!
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/06/24 12:00:36
初二全等三角形两道题速速速速速速速!
如图,已知AB=AC,AD=AE,角BAC=角DAE=90°,M是BE中点,试说明AM⊥DC
如图所示,在三角形ABC和三角形A'B'C'中,AD、A'C'分别是BC、B'C'上的中线,且AB=A'B',AC=A'C',AD=A'D',三角形ABC全等于三角形A'B'C'
![](http://img.wesiedu.com/upload/2/05/205ab45c6edba4e96d65f75985edc392.jpg)
![](http://img.wesiedu.com/upload/6/a2/6a295ddfc622a8588e5c3383753d561a.jpg)
A’B‘C’就不用我说了吧= =,A是顶点,B在左C在右,D为中点.
如图,已知AB=AC,AD=AE,角BAC=角DAE=90°,M是BE中点,试说明AM⊥DC
如图所示,在三角形ABC和三角形A'B'C'中,AD、A'C'分别是BC、B'C'上的中线,且AB=A'B',AC=A'C',AD=A'D',三角形ABC全等于三角形A'B'C'
![](http://img.wesiedu.com/upload/2/05/205ab45c6edba4e96d65f75985edc392.jpg)
![](http://img.wesiedu.com/upload/6/a2/6a295ddfc622a8588e5c3383753d561a.jpg)
A’B‘C’就不用我说了吧= =,A是顶点,B在左C在右,D为中点.
![初二全等三角形两道题速速速速速速速!](/uploads/image/z/6842227-67-7.jpg?t=%E5%88%9D%E4%BA%8C%E5%85%A8%E7%AD%89%E4%B8%89%E8%A7%92%E5%BD%A2%E4%B8%A4%E9%81%93%E9%A2%98%E9%80%9F%E9%80%9F%E9%80%9F%E9%80%9F%E9%80%9F%E9%80%9F%E9%80%9F%21)
,∠BAD=∠BAC-∠CAD=90°-∠CAD=∠DAE-∠CAD=∠CAE.
∵AM=AB+BM, AM=AE+EM=AE-ME,
∴2AM=AB+AE+(BM-ME)
∵M是BE的中点,∴BE=ME,∴2AM=AB+AE······①
而CD=AC-AD······②
①②相乘,得:
2AM·CD=AB·AC-AB·AD+AE·AC-AE·AD,
∵AB⊥AC,AD⊥AE,∴AB·AC=0,AE·AD=0,
∴2AM·CD=AE·AC-AB·AD
=AE·ACcos∠CAE-AB·ADcos∠BAD
∵AB=AC,AD=AE,∴AB=AC,AD=AE,
又∠BAD=∠CAE,∴2AM·CD=0,∴AM与CD垂直,即:AM⊥CD.
∵AM=AB+BM, AM=AE+EM=AE-ME,
∴2AM=AB+AE+(BM-ME)
∵M是BE的中点,∴BE=ME,∴2AM=AB+AE······①
而CD=AC-AD······②
①②相乘,得:
2AM·CD=AB·AC-AB·AD+AE·AC-AE·AD,
∵AB⊥AC,AD⊥AE,∴AB·AC=0,AE·AD=0,
∴2AM·CD=AE·AC-AB·AD
=AE·ACcos∠CAE-AB·ADcos∠BAD
∵AB=AC,AD=AE,∴AB=AC,AD=AE,
又∠BAD=∠CAE,∴2AM·CD=0,∴AM与CD垂直,即:AM⊥CD.