Question

give: ∠BDE ≅ ∠CDE and BD ≅ CD.
Prove ∠ABD ≅ ∠ACD

Answer 1

3) $\angle ADB$ and $\angle BDE$ are supplementary (if two angles form a linear pair, they are supplementary)

4) $\angle ADC$ and $\angle CDE$ are supplementary (if two angles form a linear pair, they are supplementary)

5) $\angle ADB \cong \angle ADC$ (supplements of congruent angles are congruent)

6) $\triangle ADB \cong \triangle ADC$ (SAS)

7) $\angle ABD \cong \angle ACD$ (CPCTC)