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 angle vith two parallal lines.
A transversal that is perpendicular to two parallal lines.

Question

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

angle vith two parallal lines.
A transversal that is perpendicular to two parallal lines.

UpStudy AI · Accepted Answer

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.**
A transversal that is perpendicular to two parallel lines provides a counterexample to the statement that alternate interior angles are never supplementary.

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