As shown in the figure, in △ ABC, BD bisects ∠ ABC, de ‖ BC intersects AB at point E, EF ‖ AC intersects BC at point F. try to guess the size relationship between be and CF, and explain the reasons, as shown in figure.doc

As shown in the figure, in △ ABC, BD bisects ∠ ABC, de ‖ BC intersects AB at point E, EF ‖ AC intersects BC at point F. try to guess the size relationship between be and CF, and explain the reasons, as shown in figure.doc

BE=CF.
∵ BD bisection ∠ ABC
∴∠EBD=∠DBC=∠ABC/2
∵DE//BC
∴∠BDE=∠DBC ∠DBC=∠DBE
∴∠BDE=∠DBE
∴BE=DE
While de / / FC EF / / DC
Fcde is a parallelogram
DE=FC
∴BE=FC