State whether the following statement is true or false.

When two lines are intersected by a transversal in a way that two alternate angles are equal, the lines are said to be parallel.

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True

False

answer is A.

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Detailed Solution

It is given that two lines are intersected by a transversal in a way that two alternate angles are equal.
We know that a transversal line intersects two other lines at two different points within the same plane. The angles that are in corresponding corners on a transversal are known as corresponding angles.

∠ 1 & ∠ 5

and

∠ 2 & ∠ 6

in the following diagram are examples of corresponding angles.
Question Image

The two lines will be parallel if the alternative angles are equal, and the reverse is also true if the lines are not parallel.
Assume that a transversal intersects two lines and that the angles at either end of the intersection are equal. The lines are parallel, in other words.
Therefore, when two lines are intersected by a transversal in a way that two alternate angles are equal, the lines are said to be parallel.
Thus, the given statement is true.
Hence, option (1) is correct.

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