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.

Explanation

(i) If two lines are intersected by a transversal, then corresponding angles are equal.
FALSE
Reason: If a transversal intersects two PARALLEL LINES then each pair of corresponding angles are equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
TRUE
Reason : If a transversal intersects two PARALLEL LINES then each pair of alternate interior angles are equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other. FALSE
Reason : Two lines perpendicular to the same line are PARALLEL to each other.
(iv) Two lines parallel to the same line are parallel to each other.
TRUE
Reason : 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.
FALSE
Reason : If a transversal intersects two PARALLEL LINES then each pair of the interior angles on the same side are supplementary (`180^@`).