# Which of the following statements are true?

Question:

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 a definite length.

(iv) A line $\overleftrightarrow{A B}$ is same as line $\overleftrightarrow{B A}$

(v) A ray $\overrightarrow{A B}$ is same as ray $\overrightarrow{B A}$.

(vi) Two distinct points always determine a unique line.
(vii) Three lines are concurrent if they have a common point.
(viii) Two 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.

Solution:

(i) False. A line segment has a definite length.

(ii) False. A ray has one end-point.

(iii) False. A line has no definite length.

(iv) True

(v) False. $\overleftrightarrow{B A}$ and $\overleftrightarrow{A B}$ have different end-points.

(vi) True

(vii) True

(viii) True

(ix) True

(x) True

(xi) False. Two lines intersect at only one point.

(xii) True