Question

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

1. If $a || b$, then $∠1 = ∠5$.
2. If $∠4 = ∠6$, then $a || b$.
3. If $∠4 + ∠5 = 180°$, then $a || b$.

Answer 1

: (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.

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(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.

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(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.