Two lines which are parallel to the same line, are parallel to each other

Theorem 6.6 : Lines which are parallel to the same line are parallel to each other.

Prove that the two lines which are both parallel to the same line are parallel to one another.

Which of the following statements are true (T) 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 angle on the same side of the transversal are equal.

prove that two lines m and n be parallel to the same given line are parallel to each other.

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

Prove that two lines perpendicular to the same line are parallel to each other.

Fill in the blanks in each of the following to make the statement true: (i) If two parallel lines are intersected by a transversal, then each pair of corresponding angles are.... (ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are... (iii) Two lines perpendicular to the same line are.... to each other. (iv) Two lines parallel to the same line are .......... to each other. (v) If a transversal intersects a pair of lines in such away that a pair of alternate angles are equal, then the line are... (vi) If a transversal intersects a pair of lines in such away that the sum of interior angles on the same side of transversal is 180,then the line are .......

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

Two straight lines are cut by a transversal. If the bisectors of a pair of co-interior angles are perpendicular to each other , prove the two straight lines are parallel to each other.