Question

eh bisects ∠feg and ef ≅ eg. complete the proof that δefh ≅ δegh.

1 eh bisects ∠feg given
2 ef ≅ eg given
3 ∠feh ≅ ∠geh definition of angle bisector
4

Explanation:

Step1: Identify shared side

$\overline{EH} \cong \overline{EH}$

Step2: State reflexive property

Reason: Reflexive Property of Congruence

Step3: Apply SAS congruence

$\triangle EFH \cong \triangle EGH$ (SAS: $\overline{EF} \cong \overline{EG}$, $\angle FEH \cong \angle GEH$, $\overline{EH} \cong \overline{EH}$)

Answer:

Statement	Reason
$\overline{EF} \cong \overline{EG}$	Given
$\angle FEH \cong \angle GEH$	Definition of angle bisector
$\overline{EH} \cong \overline{EH}$	Reflexive Property of Congruence
$\triangle EFH \cong \triangle EGH$	Side-Angle-Side (SAS) Congruence Postulate