Find all pair $(m,n)$ of integer ($m >1,n \geq 3$) with the following property:If an $n$-gon can be partitioned into $m$ isoceles triangles,then the $n$-gon has two congruent sides.
1. **Understanding the problem**: We need to find all pairs \((m, n)\) of integers such that \(m > 1\) and \(n \geq 3\), and an \(n\)-gon can be partitioned into \(m\) isosceles triangles, and the \(n\)-gon has two congruent sides.

2. **Analyzing the partitioning**: If an \(n\)-gon can be partitioned into \(m\) isosceles triangles, then the sum of the internal angles of the \(n\)-gon must be equal to the sum of the internal angles of the \(m\) isosceles triangles. The sum of the internal angles of an \(n\)-gon is \((n-2) \cdot 180^\circ\).

3. **Sum of angles in isosceles triangles**: Each isosceles triangle has two equal angles and one different angle. If we denote the equal angles by \(\alpha\) and the different angle by \(\beta\), then \(2\alpha + \beta = 180^\circ\). For \(m\) isosceles triangles, the total sum of the angles is \(m \cdot 180^\circ\).

4. **Relating \(n\) and \(m\)**: Since the sum of the internal angles of the \(n\)-gon must equal the sum of the internal angles of the \(m\) isosceles triangles, we have:
   \[
   (n-2) \cdot 180^\circ = m \cdot 180^\circ
   \]
   Simplifying, we get:
   \[
   n - 2 = m
   \]
   Therefore:
   \[
   n = m + 2
   \]

5. **Checking the condition of congruent sides**: We need to ensure that the \(n\)-gon has two congruent sides. If \(n = m + 2\), then the \(n\)-gon can be partitioned into \(m\) isosceles triangles. However, we need to verify if this partitioning guarantees two congruent sides.

6. **Constructing the \(n\)-gon**: Consider constructing the \(n\)-gon by starting with one isosceles triangle and adding more isosceles triangles such that they share sides. This construction method can ensure that at least two sides of the \(n\)-gon are congruent because each isosceles triangle has two equal sides.

7. **Conclusion**: The pairs \((m, n)\) that satisfy the given conditions are those where \(n = m + 2\) and \(m > 1\), \(n \geq 3\). This ensures that the \(n\)-gon can be partitioned into \(m\) isosceles triangles and has at least two congruent sides.

The final answer is \( \boxed{ (m, n) } \) such that \(n = m + 2\) and \(m > 1\), \(n \geq 3\).