Two lines l and m are perpendicular to the same line n. Are l and m perpendicular to each other? Give reason for your answer

Solution:

Given, the lines l and m are perpendicular to the same line n.

We have to determine if l and m are perpendicular to each other.

The lines l and m are perpendicular to n

So, ∠1 = ∠2 = 90°

From the figure,

∠1 and ∠2 are corresponding angles.

We know that when two lines are perpendicular to the same line, each of the two corresponding angles formed by these lines with the same line are equal.

Therefore, the lines l and m are not perpendicular but are parallel to each other.

✦ Try This: Can two acute angles be complementary to each other?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

NCERT Exemplar Class 9 Maths Exercise 6.2 Problem 10

Two lines l and m are perpendicular to the same line n. Are l and m perpendicular to each other? Give reason for your answer

Summary:

Two lines l and m are perpendicular to the same line n. l and m are not perpendicular to each other. The corresponding angles formed by these lines are equal. The lines l and m are parallel

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