What values for xx and yy make △mno≅△prt▵mno≅▵prt? triangles mno and prt

Unfortunately, you have not provided a diagram of the triangles, therefore, I cannot give a precise answer.
However, I can help you understand how to solve such problem and you can apply the explanation in the triangles you have.

Now, when writing congruent triangles, the order of the letters is very important. This is because each side/angle in the first triangle is congruent to the corresponding side/angle in the second one.

In the given, we have:
ΔMNO ≈ ΔPRT
This means that:
angle M = angle P
angle N = angle R
angle O = angle T
MN = PR
NO = RT
MO = PT

Now, to get x and y, all you have to do is make use of the above equal angles/sides.
Equate the corresponding angles/sides having the variables x and y and solve for them

Hope this helps :)

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !