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, $\angle 1=90°$ Also, since ​l is perpendicular to m, $\angle 2=90°$ Therefore, $\angle 1=\angle 2$ This implies that the corresponding angles are equal. Therefore, the lines m and n are parallel to each other.MathematicsRS Aggarwal (2017)Standard IX

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