Question

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 lines 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 lines are ...

Answer 1

(i) If two parallel lines are intersected by a transversal, then corresponding angles are equal.

(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are supplementary.

(iii) 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.

(v) If a transversal intersects a pair of lines in such a way that a pair of interior angles is equal, then the lines are parallel.

(vi) If a transversal intersects a pair of lines in such a way that a pair of interior angles on the same side of transversal is, then the lines are parallel.