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

the first reason is always

1. given

we also have

2. given

3. given

4. definition of congruent segments

5. definition of a segment length (i guess; a segment has the same length whichever way we list the endpoints.)

6.   addition equality postulate or some such; we added equations.

7. segment addition postulate

8. def congruent segments

9.   aas angle-angle-side congruent triangles theorem  

5

step-by-step explanation: