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 is congruent to ∠GEF. What would Ebony need to compare to make sure the triangles are congruent by AAS?

a. Segment EG and segment OM
b. ∠EFG and ∠ONM
c. Segment NM and segment FG
d. ∠EGF and ∠OMN

Answer 1

Ebony needs to compare ∠EFG and ∠ONM to ensure the triangles are congruent by AAS, as this will provide the second angle needed alongside the congruent side not included between the angles.

Step-by-step explanation:

To ensure that the triangles are congruent by the Angle-Angle-Side (AAS) Congruence Theorem, Ebony needs to compare another angle besides the one given. Since she already has one angle and one side congruent (∠MON ≅ ∠GEF and segment EF ≅ segment ON), the third piece of information she needs for AAS must be another angle that is not included in the side already known to be congruent. Therefore, the correct answer is b. ∠EFG and ∠ONM. By comparing these angles, if ∠EFG ≅ ∠ONM, she can be confident that the triangles are congruent by AAS since two angles and a non-included side are congruent.