Question

Which of the following needs to be true in order to show that ∠XYZ ≅ ∠DEF by AAS theorem?

a) ∠YZE ≅ ∠FXD
b) ∠XYZ ≅ ∠DEF
c) ∠XY = ∠DE
d) ∠YXE = ∠DXF

Answer 1

To show that ∠XYZ ≅ ∠DEF by the AAS theorem, ∠XY = ∠DE and ∠YZE ≅ ∠FXD need to be true.

Step-by-step explanation:

In order to show that ∠XYZ ≅ ∠DEF by the AAS theorem, the following needs to be true:

1. ∠XY = ∠DE: This is the angle-angle criterion, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are congruent.
2. ∠YZE ≅ ∠FXD: This is the angle-side-angle criterion, which states that if two angles and the side between them of one triangle are congruent to two angles and the side between them of another triangle, then the triangles are congruent.

Therefore, the correct answer is a) ∠XY = ∠DE and b) ∠YZE ≅ ∠FXD. The other options are not necessary to show triangle congruence by AAS.