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  • 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.

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.

Answers (1)

Answer: No.

Solution.

The two lines l and m are perpendicular to the same line n.
We can have 3 possible scenarios:
1. The lines l and m may lie on the same side of n

\angle lAn=\angle mCn=90^{\circ}
As we can see corresponding angles are equal, so l is parallel to m
l and m are not perpendicular to each other
2. The lines l and m may lie on the opposite side of n
Extend lA to point B and mC to point D

\angle lAC=\angle mCA=90^{\circ}
As we can see that interior opposite angles are equal, so l is parallel to m
l and m are not perpendicular to each other
3. The lines l and m are the same and overlap each other.
Again, l and m are not perpendicular to each other

Hence, the lines l and m are not perpendicular.

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