The congruency of △mno and △xyz can be proven using a reflection across the line bisecting oz. however, this congruency can also be proven using geometric postulates, theorems, and definitions. prove that the triangles are congruent using a two-column proof and triangle congruency theorems. given: ∠m ≅ ∠x ∠n ≅ ∠y yo ≅ nz prove: △mno ≅ △xyz

Given two triangles mno and xyz   with < m-=< x, < n-=< y and yo-=nz. the triangles are deduced to be congruent by aas (angle-angle-side) postulate which states that if there exists two corresponding angles and at least one side which is corresponding to a set of a given figure, then the figures are congruent.
therefore we can conclude that mno and xyz are congruent by aas

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