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) $overline{eg}congoverline{eg}$ $angle hegcongangle feg$ $overline{he}congoverline{fe}$ given in the diagram reflexive property of congruence angle bisectors create congruent angles

Explanation:

1. For $\overline{EG}\cong\overline{EG}$, it's the same line segment, so by the reflexive property of congruence.
2. Since $\overline{EG}$ is an angle - bisector of $\angle HEF$, by the definition of an angle - bisector, $\angle HEG\cong\angle FEG$.
3. $\overline{HE}\cong\overline{FE}$ is given in the 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