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Question

If two straight lines are perpendicular to the same line, prove that they are parallel to each other.


Solution

Let m and n be the two parallel lines perpendicular to the line l.
Since, l is perpendicular to m,
1=90°
Also, since ​l is perpendicular to m,
2=90°
Therefore, 1=2
This implies that the corresponding angles are equal.
Therefore, the lines m and n are parallel to each other.

Mathematics
RS Aggarwal (2017)
Standard IX

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