Which of the following statements are true ?
(i) A line segment has no definite length
(ii) A ray has no end point
(iii) A line has definite length
(iv) A line AB is the same as line BA
(v) A ray AB is the same as ray BA
(vi) Two distnict points always determine a unique line
(vii) Three lines are concurrent if they have a common point
(viii)T wo distinct lines cannot have more than one point in common
(ix) Two intersecting lines cannot be both parallel to the same line
(x) open half line is the same thing as ray
(xi) Two lines may intersect in two points
(xii) Two lines are parallel only when they have no point in common

Answer

To determine which of the statements are true, let's analyze each statement one by one:

1. **Statement (i)**: A line segment has no definite length.
- **Analysis**: This statement is **false**. A line segment has a definite length, which is the distance between its two endpoints.

2. **Statement (ii)**: A ray has no end point.
- **Analysis**: This statement is **false**. A ray has one endpoint (the starting point) and extends infinitely in one direction.

3. **Statement (iii)**: A line has definite length.
- **Analysis**: This statement is **false**. A line extends infinitely in both directions and does not have a definite length.

4. **Statement (iv)**: A line AB is the same as line BA.
- **Analysis**: This statement is **true**. The order of points does not affect the line; line AB is the same as line BA.

5. **Statement (v)**: A ray AB is the same as ray BA.
- **Analysis**: This statement is **false**. A ray has a fixed starting point (A) and extends infinitely in the direction of point B. Therefore, ray AB is not the same as ray BA.

6. **Statement (vi)**: Two distinct points always determine a unique line.
- **Analysis**: This statement is **true**. Any two distinct points will always define one unique line.

7. **Statement (vii)**: Three lines are concurrent if they have a common point.
- **Analysis**: This statement is **true**. If three lines intersect at a single point, they are considered concurrent.

8. **Statement (viii)**: Two distinct lines cannot have more than one point in common.
- **Analysis**: This statement is **true**. Two distinct lines can intersect at most at one point.

9. **Statement (ix)**: Two intersecting lines cannot be both parallel to the same line.
- **Analysis**: This statement is **true**. If two lines intersect, they cannot be parallel to the same line.

10. **Statement (x)**: An open half line is the same thing as a ray.
- **Analysis**: This statement is **true**. An open half line (or ray) has one endpoint and extends infinitely in one direction.

11. **Statement (xi)**: Two lines may intersect in two points.
- **Analysis**: This statement is **false**. Two lines can intersect at most at one point.

12. **Statement (xii)**: Two lines are parallel only when they have no point in common.
- **Analysis**: This statement is **true**. Parallel lines do not intersect, meaning they have no points in common.

### Summary of True Statements:
- True: (iv), (vi), (vii), (viii), (ix), (x), (xii)
- False: (i), (ii), (iii), (v), (xi)