初中几何题求教(很简单,在线等)如图,三角形ABC和三角形ADE中∠ACB=∠ADE=90°,∠BAC=∠DAE,M是BE的中点,D不在AC上,求证MD=MC (M不在AC上!M不在AC上呀!照片照不清楚而已)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 05:39:56
![初中几何题求教(很简单,在线等)如图,三角形ABC和三角形ADE中∠ACB=∠ADE=90°,∠BAC=∠DAE,M是BE的中点,D不在AC上,求证MD=MC (M不在AC上!M不在AC上呀!照片照不清楚而已)](/uploads/image/z/7848757-37-7.jpg?t=%E5%88%9D%E4%B8%AD%E5%87%A0%E4%BD%95%E9%A2%98%E6%B1%82%E6%95%99%EF%BC%88%E5%BE%88%E7%AE%80%E5%8D%95%2C%E5%9C%A8%E7%BA%BF%E7%AD%89%EF%BC%89%E5%A6%82%E5%9B%BE%2C%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E5%92%8C%E4%B8%89%E8%A7%92%E5%BD%A2ADE%E4%B8%AD%E2%88%A0ACB%3D%E2%88%A0ADE%3D90%C2%B0%2C%E2%88%A0BAC%3D%E2%88%A0DAE%2CM%E6%98%AFBE%E7%9A%84%E4%B8%AD%E7%82%B9%2CD%E4%B8%8D%E5%9C%A8AC%E4%B8%8A%2C%E6%B1%82%E8%AF%81MD%3DMC+%EF%BC%88M%E4%B8%8D%E5%9C%A8AC%E4%B8%8A%21M%E4%B8%8D%E5%9C%A8AC%E4%B8%8A%E5%91%80%21%E7%85%A7%E7%89%87%E7%85%A7%E4%B8%8D%E6%B8%85%E6%A5%9A%E8%80%8C%E5%B7%B2%EF%BC%89)
初中几何题求教(很简单,在线等)如图,三角形ABC和三角形ADE中∠ACB=∠ADE=90°,∠BAC=∠DAE,M是BE的中点,D不在AC上,求证MD=MC (M不在AC上!M不在AC上呀!照片照不清楚而已)
初中几何题求教(很简单,在线等)
如图,三角形ABC和三角形ADE中∠ACB=∠ADE=90°,∠BAC=∠DAE,M是BE的中点,D不在AC上,求证MD=MC
(M不在AC上!M不在AC上呀!照片照不清楚而已)
初中几何题求教(很简单,在线等)如图,三角形ABC和三角形ADE中∠ACB=∠ADE=90°,∠BAC=∠DAE,M是BE的中点,D不在AC上,求证MD=MC (M不在AC上!M不在AC上呀!照片照不清楚而已)
延长DM至F,使FM=DM,连结FB、FC
则△BFM≌△EDM
∴BF=ED,∠FBM=∠DEM
∵∠ACB=∠ADE=90°
∠BAC=∠DAE
∴△ABC∽∠AED
∴ED/BC=AD/AC
∴BF/BC=AD/AC
∴BF/AD=BC/AC
∵∠CBF
=∠CBE+∠FBE
=∠CBE+∠DEM
=360°-(∠BCD+∠CDE)
=360°-(90°+∠ACD+90°+∠ADC)
=180°-(∠CD+∠ADC)
=∠CAD
∴△ADC∽△BFC
∴∠ACD=∠BCF
∴∠ACD+∠ACF=∠BCF+∠ACF
即:∠FCD=∠ACB=90°
∵FM=DM
∴MC=MD=1/2DF