State whether the following statement is true or false.

Two lines that are perpendicular to another line are parallel.

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True

False

answer is A.

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Detailed Solution

It is given that two lines are perpendicular to another line.
We know that a transversal line is one that intersects two other lines at two different points on 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

The same line "n" is perpendicular to the two lines "l" and "m".
Two lines perpendicular to the same line are to each other.

In this case, the angles between them are

(shown within the figure).
Lines "l" and "m" are parallel because the corresponding angles of the lines "l" and "m" generated by transversal "n" are equal.
That is, two lines that are perpendicular to another line are parallel.
Thus, the given statement is true.
Hence, option (1) is correct.

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