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.