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 ̅ yo̅̅̅̅ ≅ nz̅̅̅̅ prove: mno ≅ xyz                           

∠m ≅ ∠x,  ∠n ≅ ∠y    given∠m + ∠n =    ∠x + ∠y    sum of equals are equals∠mon = ∠xzy            supplements of equals are equal, or in a triangle if two pairs of angles are congruent, so is the third (and skip the previous step)yo=nz                        givenyo+oz=nz+oz          adding equals to equals yz=no                        def collinear points xyz ≅    mno  angle-side-angle