State whether each of the following statements is true or false:
$(1)$ If a transversal intersects two parallel lines,then the interior angles on the same side of the transversal are equal.
$(2)$ The maximum number of acute angles in any triangle is two.
$(1)$ If a transversal intersects two parallel lines,then the interior angles on the same side of the transversal are equal.
$(2)$ The maximum number of acute angles in any triangle is two.
(B) $(1)$ False. If a transversal intersects two parallel lines,the interior angles on the same side of the transversal are supplementary (their sum is $180^{\circ}$),not equal.
$(2)$ False. In any triangle,the sum of all three angles is $180^{\circ}$. It is possible for all three angles to be acute (e.g.,in an equilateral triangle,all angles are $60^{\circ}$),so the maximum number of acute angles in a triangle is three.
$(2)$ False. In any triangle,the sum of all three angles is $180^{\circ}$. It is possible for all three angles to be acute (e.g.,in an equilateral triangle,all angles are $60^{\circ}$),so the maximum number of acute angles in a triangle is three.
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