如图,D是△ABC的边AB上一点,DF交AC于点E,DE=FE,FC∥AB,求证:△ADE≌△CFE.

问题描述:

如图,D是△ABC的边AB上一点,DF交AC于点E,DE=FE,FC∥AB,求证:△ADE≌△CFE.

证明:∵FC∥AB,
∴∠ADE=∠CFE.
在△ADE和△CFE中,
∠ADE=∠CFE,DE=FE,∠AED=∠CEF.
∴△ADE≌△CFE.