Question 1-20 Which situation would provide a counterekample to the statement below? Alternate interior angles are nover supplementary. A line that has a slope equal to the slopes of two parallel lines. A line that is parallel to two parallel lines. A transveral that foms \( 45^{\circ} \) angle vith two parallal lines. A transversal that is perpendicular to two parallal lines.

To determine which situation would provide a counterexample to the statement "Alternate interior angles are never supplementary," we need to analyze each option in relation to the definition of alternate interior angles and their properties. 1. **A line that has a slope equal to the slopes of two parallel lines.** - This does not provide a counterexample because it simply describes a line that is parallel to two other lines. It does not address the angles formed. 2. **A line that is parallel to two parallel lines.** - Similar to the first option, this does not create any angles that would be supplementary. It just describes a parallel relationship. 3. **A transversal that forms a \( 45^{\circ} \) angle with two parallel lines.** - This situation describes a transversal intersecting two parallel lines, creating alternate interior angles of \( 45^{\circ} \). Since \( 45^{\circ} + 45^{\circ} = 90^{\circ} \), this does not provide a counterexample. 4. **A transversal that is perpendicular to two parallel lines.** - If a transversal is perpendicular to two parallel lines, it forms alternate interior angles of \( 90^{\circ} \). Since \( 90^{\circ} + 90^{\circ} = 180^{\circ} \), this means the alternate interior angles are supplementary. This situation provides a counterexample to the statement. Thus, the correct answer is: **A transversal that is perpendicular to two parallel lines.**