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In this problem, we are given triangle \( \triangle MNO \) where:

- \( \angle O \cong \angle N \) (i.e., the angles at \( O \) and \( N \) are congruent),
- \( MN = 20 \),
- \( NO = 14 \),
- We are asked to find \( OM \) (the length of side \( OM \)).

Since \( \angle O \cong \angle N \), the triangle \( \triangle MNO \) is **isosceles** with \( OM = MN \). 

Therefore, \( OM = 20 \). 

Would you like a detailed explanation of the reasoning behind this conclusion or have further questions? Here are some related questions that can deepen your understanding:

1. How do we identify that a triangle is isosceles based on angle congruence?
2. Can you explain why two sides of an isosceles triangle are equal?
3. What is the significance of congruent angles in triangle properties?
4. How would the solution change if the triangle were not isosceles?
5. What other properties of isosceles triangles can we use in similar problems?

**Tip:** In isosceles triangles, knowing two congruent angles often leads directly to knowing which sides are equal!

In triangle MNO, where angle O is congruent to angle N, MN = 20, and NO = 14. Find OM.

Solve the problem of finding OM in triangle MNO, where angle O is congruent to angle N, MN = 20, and NO = 14. This problem demonstrates the properties of isosceles triangles and is suitable for students in Grades 7-10.

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