Read the statements carefully and select the correct option.
Statement I: The line segment joining a vertex of a triangle to the mid point of its opposite side called the median of the triangle.
Statement II: If the exterior angle of a tiangle is a right angle, then each opposite interior angle is an obtuse angle.

Options

A. Both Statement -I and Statement -II are true.
B. Both Statement -I and Staement -II are false.
C. Statement -I is true but Statement -II is false.
D. Statement -I is false but Statement -II is true.

Explanation

To solve the problem, we need to analyze both statements provided in the question.

### Step-by-Step Solution:

1. **Analyze Statement I**:
- The statement says, "The line segment joining a vertex of a triangle to the midpoint of its opposite side is called the median of the triangle."
- This is a well-known definition in geometry. The median of a triangle is indeed the line segment that connects a vertex to the midpoint of the opposite side.
- **Conclusion**: Statement I is **True**.

2. **Analyze Statement II**:
- The statement says, "If the exterior angle of a triangle is a right angle, then each opposite interior angle is an obtuse angle."
- An exterior angle of a triangle is equal to the sum of the two opposite interior angles. If the exterior angle is 90 degrees, we can denote the two opposite interior angles as \( a \) and \( b \).
- According to the property of exterior angles:
\[ \text{Exterior Angle} = a + b \]
Thus, if the exterior angle is 90 degrees:
\[ a + b = 90^\circ \]
- Since both \( a \) and \( b \) must be less than 90 degrees (as they add up to 90), they cannot be obtuse (which is defined as greater than 90 degrees).
- **Conclusion**: Statement II is **False**.

3. **Final Conclusion**:
- Since Statement I is True and Statement II is False, the correct option is:
- **Option C**: Statement I is true but Statement II is false.