Question

如图所示，已知：AE垂直于AB,AF垂直于AC,AE=AB,AF=AC. 求证：(1)EC=BF;

如图所示，已知：AE垂直于AB,AF垂直于AC,AE=AB,AF=AC.
求证：(1)EC=BF;(2)EC垂直于BF

Answer 1

 

Answer 2

∵AE丄AB，AF丄AC
∴∠BAE=∠CAF=90°
∴∠BAE+∠BAC=∠CAF+∠BAC
即∠CAE=∠FAB
∵AE=AB
∠CAE=∠FAB
AC=AF
∴∆CAE全等∆FAB
∴EC=BF，∠ACE=∠AFB
∵∠ACE+∠CMF=∠AFB+∠CAF
∴∠CMF=∠CAF=90°
∴EC丄BF

Answer 3

 

Answer 4