State whether the following statement is true or false.

If two parallel lines are intersected by a transversal, then interior angles on the identical side of the transversal are supplementary.

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True

False

answer is A.

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Detailed Solution

It is given that two parallel lines are intersected by a transversal.
We know that transversal could be a line that passes through two lines at two distinct points within the same plane.
The angles in corresponding corners on a transversal are known as corresponding angles.
Within the given figure,

∠ 1 & ∠ 5

and

∠ 2 & ∠ 6

are corresponding angles.
Question Image

In the given figure,

∠ 3

and

∠ 6

are co-interior angles.
Since the lines are parallel and angles

∠ 2 & ∠ 6

are corresponding angles, they're equal.
Since angles

∠ 2 & ∠ 3

are a linear pair, the sum of angles

∠ 2 & ∠ 3

180 ° .

Therefore, the sum of angles

∠ 3

and

∠ 6

180 ° .

So, the sum of co-interior angles are

180 ° .

That is, the angles are supplementary.
Thus, if two parallel lines are intersected by a transversal, then interior angles on the identical side of the transversal are supplementary.
Thus, the given statement is true.
Hence, option (1) is correct.

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