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question 1-3
\all angles formed by parallel lines crossed by a transversal are congruent.\
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:

Step1: Recall angle properties

When parallel lines are cut by a transversal, vertical angles (A) are congruent, corresponding angles (B) are congruent, alternate interior angles (C) are congruent. Same - side interior angles (D) are supplementary (sum to \(180^\circ\)), not congruent (unless they are both \(90^\circ\)).

Step2: Analyze each option

• Option A: Vertical angles formed by intersecting lines (including transversal with parallel lines) are congruent, so not a counterexample.
• Option B: Corresponding angles with parallel lines and transversal are congruent, not a counterexample.
• Option C: Alternate interior angles with parallel lines and transversal are congruent, not a counterexample.
• Option D: Same - side interior angles formed by parallel lines and a transversal are supplementary (\( \angle 1+\angle 2 = 180^\circ\)). If one angle is \(60^\circ\) and the other is \(120^\circ\), they are not congruent, so this is a counterexample.

Answer:

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