1. **Problem statement:** Determine if triangle BED is equilateral given that angles at B and E adjacent to diagonal BE are 60° each and sides BD and DE are equal. 2. **Given:** $\angle B = 60^\circ$, $\angle E = 60^\circ$, and $BD = DE$. 3. **Recall:** An equilateral triangle has all three sides equal and all three angles equal to 60°. 4. **Analyze triangle BED:** Since $BD = DE$, triangle BED is isosceles with base BE. 5. **Sum of angles in triangle BED:** $$\angle B + \angle E + \angle D = 180^\circ$$ 6. Substitute known angles: $$60^\circ + 60^\circ + \angle D = 180^\circ$$ 7. Solve for $\angle D$: $$\angle D = 180^\circ - 120^\circ = 60^\circ$$ 8. **Conclusion:** All three angles in triangle BED are 60°, and since $BD = DE$, and $BE$ is the base, the triangle is equilateral because all sides are equal. **Final answer:** Yes, triangle BED is equilateral.