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Q.

Tell whether the following statement is true or false:

If I, m, n are three lines such that l || m and $n ⊥ l,$ Then $n ⊥ m$ .

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a

True

b

False

answer is A.

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Detailed Solution

Given a figure in which l || m and

n ⊥ l

.

If l, m, n are three lines such that l || m and n ⊥ l, then prove that n ⊥ m. from Mathematics Lines and Angles Class 9 Assam Board

In the figure, line n is the transversal to the lines l and m.
Corresponding angle property states that if a transversal intersects two parallel lines, the corresponding angles will be always equal.
Apply the property of corresponding angles in transversal n.
Since line n is perpendicular to the line l, therefore,

∠ 1 = 90 ∘

.
Since lines, l and m are parallel, therefore, their corresponding angles will be equal.
Therefore,

∠ 1

and

∠ 2

are equal.
Hence,

∠ 2 = 90 °

.
Therefore, lines n and m are perpendiculars.
Given statement is true.
Hence, option 1 is correct.

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