如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE

来源:学生作业帮助网 编辑:作业帮 时间:2024/10/06 02:00:48
如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE
xj@_e](df;J}}䣉nlV ""mmЇX&^ N>v T/3?9gC?;-z%yNUov[].iٯIFSuڕ`t] g#M5&í?ɷM4zBQilo2)~K24A^*s„9 壋*q<"00; 2 g/h^ZCf V>#ǘZGt61E,9bi/:b[UrtYfto'Նu C߼M{nXJ k8^9bꯁ{o}p[@².A8>?czrO诮+

如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE
如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE

如图,已知AB=AC,AD=AE,BD=CE.试说明:∠BAC=∠DAE
证明
∵AB=AC,AD=AE,BD=CE
∴ΔBAD≌ΔCAD(三组对边分别相等的三角形全等)
∴∠BAD=∠CAD
∠BAC=∠BAD+∠DAC
=∠CAD+∠DAC
=∠DAE
证毕!

∵AB=AC,BD=CE,AD=AE
∴△ABD≌△ACE
∴∠BAD=∠CAE
又∵∠BAC=∠BAD+∠CAD,∠DAE=∠CAE+∠CAD
∴∠BAD=∠DAE

∵AB=AC

AD=AE

BD=CE

∴△ABD≌△ACE(SSS)

∴∠BAD=∠CAE

∴∠BAD+∠DAC=∠DAC+∠ACE

即∠BAC=∠DAE

收起