To determine the relationship of the sides in triangle \( \triangle MNO \) based on the Pythagorean Theorem, we first need to know whether the triangle is a right triangle. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (\( c \)) is equal to the sum of the squares of the lengths of the other two sides (\( a \) and \( b \)):
\[ a^2 + b^2 = c^2 \]
Assuming \( MN \) and \( MO \) are the two sides forming the right angle (legs), and \( NO \) is the hypotenuse, then according to the Pythagorean Theorem, we have:
\[ MN^2 + MO^2 = NO^2 \]
If you want to express it in the form you provided, it would be:
\[ m^2 + n^2 = o^2 \]
where \( m \) and \( n \) are the lengths of the legs of the triangle, and \( o \) is the length of the hypotenuse. If you need further clarification or information specific to the triangle \( MNO \) you mentioned, please provide the details of the triangle.