Question

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:

To find a counterexample, we analyze each option:

• Vertical angles (A) are always congruent.
• Corresponding angles (B) with parallel lines are congruent.
• Alternate interior angles (C) with parallel lines are congruent.
• Same - side interior angles (D) with parallel lines are supplementary (sum to \(180^{\circ}\)), not necessarily congruent (e.g., one \(100^{\circ}\), one \(80^{\circ}\)). So this is a counterexample.

Answer:

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