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.

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Updated on: 10-Oct-2022

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