Question

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°$, then $ a//b$.

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Answer 1

(i) If $a//b$, then $\angle 1=\angle 5$

As $a//b$, so, the pair of corresponding angles are equal.

Hence, the property used here is the corresponding angles property in the above statement.

(ii) If $\angle 4=\angle 6$, then $a//b$

As $a//b$, so, the alternate interior angles will be equal.

Hence, the property used here is the alternate interior angles property in the above statement.

(iii) If $\angle 4+\angle 5=180°$, then $a//b$.

As $a//b$, so, the pair of interior angles on the same side of the transversal are supplementary,i.e., their sum is equal to $180°$.

Hence, the property used here is interior angles on the same side of the transversal are supplementary.