Question

如图,在△ABC中,∠A=90°,AB=AC,D为BC中点

Answer 1

由题意可知△ABC为等腰直角△,

∴∠ABC=∠ACB=∠BAD=∠CAD=45°,BD=CD=AD

1）∠ABC=∠CAD；BD=AD；BE=AF

∴△BED≌△AFD

∴ED=FD,∴△DEF为等腰△

2）结论仍然成立.

∵∠ABC=∠CAD=45°,∴∠DBE=∠DAF=135°

BD=AD；BE=AF

∴△DBE≌△DAF,∴DE=DF.得证.

3）∵AB=AC,BE=AF

∴AE=CF

Rt△AFE中,AE²+AF²=EF²

∴BE²+CF²=EF²