As shown in the figure, in the triangle ABC, the angle a is equal to 60 degrees It is known that, as shown in the figure, in the triangle ABC, the angles a are equal to 60 degrees CE and BF are bisectors of the triangle ABC angles and intersect at point D Prove that De is equal to DF

As shown in the figure, in the triangle ABC, the angle a is equal to 60 degrees It is known that, as shown in the figure, in the triangle ABC, the angles a are equal to 60 degrees CE and BF are bisectors of the triangle ABC angles and intersect at point D Prove that De is equal to DF

It is proved that ∵ BD and CB divide ∵ ABC and ∵ ABC equally,
∴∠DBC+∠DCB=1/2(∠ABC+∠ACB)
=1/2(180°-∠A)=60°,
∴∠AOB=120°,∠BDE=∠CDF=60°,
Intercept BG = be on BC and connect DG,
∵BE=BG,∠DBE=∠DBG,BD=BD,
∴ΔBDE≌ΔBDG,
∴DE=DG,∠BDG=∠BDE=60°,
∴∠CDG=60°=∠CDF,
And ∠ DCG = ∠ DCF, CD = CD,
∴ΔCDG≌ΔCDF,
∴DG=DF,
∴DE=DF.