: (i) Given, \(a||b\) then \(\angle 1 = ∠5\) [Corresponding angles]
If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
(ii) Given, \(∠4 = ∠6\), then \(a||b\) [Alternate interior angles]
When a transversal cuts two lines such that pairs of alternate interior angles are equal, the lines have to be parallel.
(iii) Given, \(∠4 + ∠5\) = \(180\degree\) then \(a||b\) [Co-interior]
When a transversal cuts two lines, such that pairs of interior angles on the same side of transversal are supplementary, the lines have to be parallel.