question_answer 1)

State the property that is used in each of the following statements (i) if \[a||b,\]then \[\angle 1=\angle 5.\] (ii) if \[\angle 4=\angle 6,\]then \[a||b.\] (iii) if \[\angle 4+\angle 5={{180}^{o}},\]then \[a||b\].

Answer:

(i) If two parallel lines are cut by a transversal the corresponding angles have equal measure. (ii) If two parallel lines are cut by a transversal, the alternate interior angles are equal. (iii) If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary.