Question

question 1-3
\all angles formed by parallel lines crossed by a transversal are con...\
provide a counterexample to show that this statement is not always true.
a pair of vertical angles formed by intersecting lines
a pair of corresponding angles formed by parallel lines and a transversal
a pair of alternate interior angles formed by parallel lines and a transversal
a pair of same - side interior angles formed by parallel lines and a transversal

Explanation:

To find a counterexample, we analyze each option:

• Option A: Vertical angles formed by intersecting lines are equal, but this is about intersecting lines, not parallel lines with a transversal, so not relevant.
• Option B: Corresponding angles formed by parallel lines and a transversal are congruent, so this supports the statement, not a counterexample.
• Option C: Alternate interior angles formed by parallel lines and a transversal are congruent, so this supports the statement, not a counterexample.
• Option D: Same - side interior angles formed by parallel lines and a transversal are supplementary (their sum is \(180^{\circ}\)), not congruent (unless each is \(90^{\circ}\)). So a pair of same - side interior angles formed by parallel lines and a transversal can have different measures (e.g., one is \(100^{\circ}\) and the other is \(80^{\circ}\)), which shows the statement "All angles formed by parallel lines crossed by a transversal are congruent" is not always true.

Answer:

D. A pair of same - side interior angles formed by parallel lines and a transversal