Question

caroline is given this diagram and told that $overline{eg}$ is an angle bisector of $angle hef$. she looks carefully and finds one pair of congruent angles between two pairs of congruent sides. she determines that the triangles must be congruent by the sas congruent theorem. match each pair of congruent corresponding parts with the reason caroline knows that they are congruent (1 point) $overline{eg}congoverline{eg}$ reflexive property of congruence $angle hegcongangle feg$ angle bisectors create congruent angles $overline{he}congoverline{fe}$ given in the diagram

Explanation:

1. $\overline{EG}\cong\overline{EG}$ because any segment is congruent to itself, which is the reflexive property of congruence.
2. Since $\overline{EG}$ is an angle - bisector of $\angle HEF$, by the definition of an angle - bisector, it creates two congruent angles $\angle HEG\cong\angle FEG$.
3. The congruence of $\overline{HE}\cong\overline{FE}$ is indicated by the tick - marks in the given diagram.

Answer:

$\overline{EG}\cong\overline{EG}$ - Reflexive Property of Congruence
$\angle HEG\cong\angle FEG$ - Angle Bisectors create congruent angles
$\overline{HE}\cong\overline{FE}$ - Given in the diagram