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State whether the following is true or false.

If two lines $l$ and m are perpendicular to the same line, then $l$ and m are perpendicular to each other.

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True

False

answer is B.

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Detailed Solution

Given, two lines

and m are perpendicular to the same line.
We know that two lines are said to be perpendicular if they intersect at right angle or

90 o

and vice-versa.
Drawing the required diagram,
Question Image

From the figure,

l

and

m

are the two perpendiculars to the line

n

, i.e.,

n

is the transversal passing through the lines

l

and

m

forming angles

∠ 1

and

∠ 2

.
Check whether

l

and

m

perpendicular to each other. By definition of corresponding angles,

∠ 1

and

∠ 2

are corresponding angles.
Since,

l ⊥ n

so,

∠ 1 = ∠ 2 = 90 °

i.e. the corresponding angles

∠ 1

and

∠ 2

formed by the transversal

n

to the lines

l

and

m

are equal.
Thus, the lines

l

and

m

in the given problem are not perpendicular but

l ∥ m

.
Hence, the given statement is false.
Therefore, option (2) is correct.

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