Question

ebony is cutting dough for pastries in her bakery. she needs all the pieces to be congruent triangles and has ensured that $overline{ef}congoverline{on}$ and $angle moncongangle gef$. what would ebony need to compare in order to make sure the triangles are congruent by sas?
$overline{om}$ and $overline{ef}$
$overline{eg}$ and $overline{om}$
$overline{nm}$ and $overline{fg}$
$overline{eg}$ and $overline{mn}$

Explanation:

Step1: Recall SAS congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. We are given that $\overline{EF}\cong\overline{ON}$ and $\angle MON\cong\angle GEF$. The included angles $\angle MON$ and $\angle GEF$ are between sides $\overline{OM},\overline{MN}$ and $\overline{EG},\overline{EF}$ respectively. Since $\overline{EF}\cong\overline{ON}$, we need to find the side - pair such that the included angles are the given congruent angles. The side that is part of the angle - side relationship for the given congruent angles and is left to compare is $\overline{EG}$ and $\overline{MN}$.

Answer:

D. $\overline{EG}$ and $\overline{MN}$