Question

Ebony is cutting dough for pastries in her bakery. She needs all the pieces to be congruent triangles and has ensured that segment EF ≅ segment ON and ∠MON ≅ ∠GEF. What would Ebony need to compare in order to make sure the triangles are congruent by ASA?

1) Segment EG and segment OM
2) ∠EFG and ∠ONM
3) Segment NM and segment FG
4) ∠EGF and ∠OMN

Answer 1

The correct comparison Ebony would need to make to ensure the triangles are congruent by ASA is: 4). ∠EGF and ∠OMN

Step-by-step explanation:

To prove the triangles congruent by ASA (Angle-Side-Angle), Ebony needs to compare corresponding angles and the included side of both triangles. In this case, ∠EGF and ∠OMN are the corresponding angles, and they have already been established as congruent.

Next, we need to ensure that the included sides are congruent. The given information states that segment EF ≅ segment ON. Therefore, the side opposite the congruent angles is equal in both triangles.

In summary, Ebony needs to compare ∠EGF and ∠OMN to confirm that the angles are congruent, and she has already confirmed that the included sides EF and ON are equal. This satisfies the conditions for ASA, proving the triangles congruent.