The specified triangles PQR and MNO are: not similar.
How to identify if two given triangles are similar or not?
How to identify
Two triangles are similar if their corresponding sides are scaled version(second triangle's sides being obtainable by multiplying one triangle's side by a single common constant(same for all three sides).
Similar triangles have corresponding angles of same measurement.
You can think of similar triangles as if you zoomed-in or zoomed-out one triangle to get the other one. This can change sides' lengths but not the angles.
Suppose that if two triangles ABC and DEF are said to be similar(remember, naming order matters here. ABC and DEF cannot be written BAC and DEF etc. The order shows what are the corresponding pairs. They, if written in a way that corresponding sides are same, then ordering can be done. Like BAC and EDF are similar), then we have:
[tex]m\angle A =m\angle D\\m\angle B = m\angle E\\m\angle C = m\angle F[/tex] (internal angles, m denotes that its measurement of those angles).
and
[tex]|AB| = k \times |DE|\\|AC| = k \times |DF|\\|BC| = k \times |EF|[/tex]
where k is a constant number, and |AB| means length of line segment AB.
For the given case, if PQR and MNO would be similar, then the internal angles at Q and N had to be of same measure.
Using the fact that all angles of a triangle sum to 180 degrees, we can see that neither Q, nor R is of 45 degrees(we need to check this fact that if ordering is differing or actually the angles are not same, because it would've happened that Q is equal to O and R is equal to N, but in this case, none of Q and R is equal to N)(we're not considering P and M as they're equal and of 90 degrees).
Thus, the triangles PQR and MNO are not similar to each other.
Learn more about similarity of triangles here:
https://brainly.com/question/11929676
