The difference of any two sides of a triangle is _______ than the third side .

Answer

To solve the question, we need to understand a fundamental property of triangles regarding their sides.

### Step-by-Step Solution:

1. **Understanding the Triangle Inequality Theorem**:
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This can be expressed as:
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)

2. **Considering the Difference of Two Sides**:
Let's denote the sides of the triangle as \( a \), \( b \), and \( c \). We can consider the difference between any two sides, say \( a \) and \( b \). The difference can be expressed as \( |a - b| \).

3. **Applying the Triangle Inequality**:
According to the triangle inequality theorem, we know that:
- \( a + b > c \)
- Rearranging this gives us \( a + b - c > 0 \) or \( a + b > c \).
- Similarly, we can derive that \( |a - b| < c \). This means that the absolute difference between any two sides of the triangle is less than the length of the third side.

4. **Conclusion**:
Therefore, we can conclude that the difference of any two sides of a triangle is always **less than** the third side.

### Final Answer:
The difference of any two sides of a triangle is **less than** the third side.