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)