Answer:
Step-by-step explanation:
Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.
Proof
AB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon
∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon
ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence
FB ≅ BD ≅ DF . . . . CPCTC
ΔBDF is equilateral . . . . definition of equilateral triangle
