Use the AAS congruence rule to prove that the two given triangles are congruent.
The congruence of two of the corresponding angles is already given:
[tex]\begin{gathered} \angle M\approx\angle X \\ \\ \angle N\approx\angle Y \end{gathered}[/tex]
On the other hand, since O and Z lie in the segment YN, we know that:
[tex]\begin{gathered} YO+ON=YN \\ \\ NZ+ZY=YN \end{gathered}[/tex]
And since YO=NZ (given), then:
[tex]YZ=ON[/tex]
Since two angles and one pair of corresponding sides are congruent, then, using the AAS correspondence rule, we can conclude that the triangles MNO and XYZ are congruent.
