Which of the following statements are true (T) and which are false (F) ? Give reasons.

iv. Two lines parallel to the same line are parallel to each other.

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Solution

Lines which are parallel to the same line are parallel to each other.

For example,
If $A B ∥ P Q and E F ∥ P Q then A B ∥ E F$

Hence, the given statement is true.

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Similar questions

Which of the following statements are true (I) and which are false (F)? Give reasons.
(i) If two lines are intersected by a transversal, then corresponding angles are equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other.
(iv) Two lines parallel to the same line are parallel to each other.
(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

Q. Which of the following statements are true and which are false?
(i) Two lines are parallel if they do not meet, even when produced.
(ii) Two parallel lines are everywhere the same distance apart.
(iii) If two line segments do not intersect, they are parallel.
(iv) If two rays do not intersect, they are parallel.

Q. State which of the following statements are true (T) or which are false (F):

(i) If two lines in the same plane do not interest, then they much be parallel.
(ii) Distance between two parallel lines is not same every where.
(iii) If m ⊥ i, n ⊥ i and m ≠ n, then m ∥ n.
(iv) Two non-intersection coplanar rays are parallel.
(v) If ray AB ∥ line , then line segment AB ∥ m.
(vi) If line AB ∥ line , then line segment AB ∥ m.
(vii) No two parallel segments intersect.
(viii) Every pair of lines is a pair of coplanar lines.
(ix) Two lines perpendicular to the same line are parallel.
(x) A line perpendicular to one of two parallel lines is perpendicular to the other.

Q. Which of the following statements are true (T) and which are false (F) ? Give reasons.

iii. Two lines perpendicular to the same line are perpendicular to each other.

Q. Fill in the blank in each of the following to make the statement true:

iv. Two lines parallel to the same lines are to each other.

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Perpendicular to a Line

Standard VI Mathematics

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Which of the following statements are true (T) and which are false (F) ? Give reasons.​ iv. Two lines parallel to the same line are parallel to each other.​

Lines which are parallel to the same line are parallel to each other.​ ​For example,​ If AB∥PQ and EF∥PQ then AB∥EF ​Hence, the given statement is true. ​

Which of the following statements are true (T) and which are false (F) ? Give reasons.

iv. Two lines parallel to the same line are parallel to each other.

Lines which are parallel to the same line are parallel to each other.

For example,
If $A B ∥ P Q and E F ∥ P Q then A B ∥ E F$

Hence, the given statement is true.