$A$ transversal intersects two lines in such a way that the two interior angles on the same side of the transversal are equal. Will the two lines always be parallel? Give reason for your answer.
(NO) No,the two lines will not always be parallel. For two lines to be parallel,the sum of the interior angles on the same side of the transversal must be $180^{\circ}$. If each of the two equal interior angles is $x$,then their sum is $x + x = 2x$. The lines are parallel only if $2x = 180^{\circ}$,which means $x = 90^{\circ}$. If $x \neq 90^{\circ}$,the lines are not parallel.
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