如图,已知AB=AC,AB⊥BD,AC⊥CD,AD和BC相交于点E.求证:(1)CE=BE.(2)BC⊥AD

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/29 15:22:46
如图,已知AB=AC,AB⊥BD,AC⊥CD,AD和BC相交于点E.求证:(1)CE=BE.(2)BC⊥AD
xNA_ee kzyRt<@4]v7]\4ZrC!ȣ8 Tgϙ^69N&?M?0Nh1^;ńU9pb|y<|?_ޮ6Ѳ) = 77

如图,已知AB=AC,AB⊥BD,AC⊥CD,AD和BC相交于点E.求证:(1)CE=BE.(2)BC⊥AD
如图,已知AB=AC,AB⊥BD,AC⊥CD,AD和BC相交于点E.求证:(1)CE=BE.(2)BC⊥AD

如图,已知AB=AC,AB⊥BD,AC⊥CD,AD和BC相交于点E.求证:(1)CE=BE.(2)BC⊥AD
∵AB=AC AB⊥BD AD=AD
∴△ABD≌△ACD (HL)
∴CD=BD ∠CDA=∠BDA 且 ED=ED
∴△CDE≌△BDE (SAS)
∴CE=BE ∠CED=∠BED
∵ ∠CED=∠BED 且 ∠CED+∠BED=180°
∴ ∠CED=∠BED=90°
∴BC⊥AD