Question

what is the student’s error? given ∠1 ≅ ∠2. by the vertical angles thm., ∠1 ≅ ∠3, so by the transitive property, ∠2 ≅ ∠3. by the converse of the corresponding angles thm., a || b. x choose the correct answer below. a. converse of the corresponding angles theorem was used. b. ∠2 and ∠3 are not corresponding angles. c. ∠2 and ∠3 are not vertical angles. d. m∠1 ≠ m∠3

Explanation:

To determine the student's error, analyze each option:

• Option A: The Converse of Corresponding Angles Thm is valid if angles are corresponding, so this isn’t the error.
• Option B: For the Converse of Corresponding Angles Thm, \( \angle 2 \) and \( \angle 3 \) are not corresponding angles (corresponding angles are in the same relative position at each intersection). So using the theorem here is incorrect because \( \angle 2 \) and \( \angle 3 \) don’t satisfy the “corresponding” condition.
• Option C: \( \angle 1 \) and \( \angle 3 \) are vertical angles (so \( \angle 1 \cong \angle 3 \)), but the error isn’t about vertical angles of \( \angle 2 \) and \( \angle 3 \) (they aren’t vertical angles, but that’s not the key error here).
• Option D: By Vertical Angles Thm, \( m\angle 1 = m\angle 3 \), so this is false.

The key error is that \( \angle 2 \) and \( \angle 3 \) are not corresponding angles, making the application of the Converse of Corresponding Angles Thm invalid.

Answer:

B. \( \angle 2 \) and \( \angle 3 \) are not corresponding angles.