Two lines are repectively perpendicular to two parallel lines. Show that they are parallel to each other.

Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.

Transversal to two parallel lines:

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 that are respectively perpendicular to two intersecting lines intersect each other.

Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other .

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

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

For what value of x will the lines l and m be parallel to each other ?