Answer:
Δ MNO ≅ ΔXYZ by AAS postulate.
Step-by-step explanation:
Given:
[tex]\angle M=\angle X[/tex], [tex]\angle N=\angle Y[/tex], and YO = NZ.
Consider YO = NZ
Add OZ on both sides
YO + OZ = NZ + OZ
YZ = NO
Consider triangles Δ MNO and ΔXYZ.
Statement Reason
1. [tex]\angle M=\angle X[/tex] Given
2. [tex]\angle N=\angle Y[/tex] Given
3. YZ = NO ∵ YO = NZ
Therefore, the two triangles Δ MNO and ΔXYZ are congruent to each other from AAS postulate as two corresponding angles and a corresponding side are equal to each other.