**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