State the property that is used in each of the following statements?

(i) If a||b, then ∠1 = ∠5

(ii) If ∠4 = ∠6, then a|| b.

(iii) If ∠4 +∠5 = 180 ^{o} then a|| b.

(i) From the above given figure it is clear that,

∠1 = ∠5

This is because a is parallel to b also ∠1 and ∠5 are corresponding angles

Hence,

In these angles are equal due to corresponding angles property

(ii) From the above given figure, it is clear that,

∠4 = ∠6

This is because of the alternate interior angles property

(iii) We have,

From the above given figure, it is clear that,

∠4 + ∠5 = 180^{o}

Because we know that, the interior angles on the same side of the transversal are supplementary

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