Two lines l and m are perpendicular to the sa | vedclass

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Question

(B) When two lines $l$ and $m$ are perpendicular to the same line $n$,the interior angles on the same side of the transversal $n$ are both $90^{\circ}

Vedclass · Accepted Answer

No,they are parallel to each other.

Vedclass · Answer

(B) When two lines $l$ and $m$ are perpendicular to the same line $n$,the interior angles on the same side of the transversal $n$ are both $90^{\circ}$.The sum of these interior angles is $90^{\circ} + 90^{\circ} = 180^{\circ}$.According to the property of parallel lines,if the sum of interior angles on the same side of a transversal is $180^{\circ}$,then the lines are parallel.Therefore,the lines $l$ and $m$ are parallel to each other,not perpendicular.

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.

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