Answer: C.[tex]\angle{B}\cong\angle{Y}[/tex]
Step-by-step explanation:
- AAS theorem says that if two angles and a non-included side of a triangle are congruent to two angles and a non-included side of other triangle then the triangles are congruent.
In the given picture , we have ΔABC and ΔXYZ
Given : [tex]\angle{A}\cong\angle{X}[/tex]
[tex]\overline{AC}\cong\overline{XZ}[/tex]
To show both the triangles are congruent by AAS theorem , we need one more angle such that the given sides must remains non-included.
Thus, [tex]\angle{B}[/tex] must be congruent to [tex]\angle{Y}[/tex] to show ΔABC ≅ ΔXYZ by AAS.
[If we take [tex]\angle{C}\cong\angle{Z}[/tex], then the triangles are congruent by ASA]
