Answer
1. Given
2. Definition of congruent angles
3. Definition of angle bisectors
4. Division Property of Equality
5. Substitution
6. Definition of congruent angles
Work Step by Step
1. $\angle ABC\cong \angle EFG$
2. $m\angle ABC=m\angle EFG$ (if two angles are congruent, they have the same angle measure)
3. $m\angle 1=m\angle 2=\frac{m\angle ABC}{2}$ and $m\angle 3=m\angle 4=\frac{m\angle EFG}{2}$ As both $BD$ and $FH$ are bisectors.
4. $\frac{m\angle ABC}{2}=\frac{m\angle EFG}{2}$ (Dividing both sides by 2 of the equation in statement (2.)
5. $m\angle 1=m\angle 2=m\angle 3=m\angle 4$
6. $\angle 1\cong \angle 2\cong \angle 3\cong \angle 4$
(two angles are congruent if they have the same angle measure)
