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State the property that is used in each of the following statements?
$(i)$ If $a || b$
To do:
We have to state the property that is used in each of the given statements.
Solution:
(i) Given $a \| b$
We know that pairs of corresponding angles are equal if two lines are parallel.
Therefore,
$\angle1=\angle5$
Corresponding angles property is used in the given statement.
(ii) Given $\angle 4=\angle 6$
If the pair of alternate angles are equal, then the lines are parallel
Therefore,
$a \| b$
Corresponding angles property is used in the given statement.
(iii) Given $\angle4+\angle5=180^{\circ}$
If the sum of interior angles is $180^{\circ}$, then the lines are parallel
Therefore,
$a \| b$
Interior angles on the same side of the transversal are supplementary.