Question

what is the students 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. choose the correct answer below. a. ∠2 and ∠3 are not corresponding angles. b. ∠2 and ∠3 are not vertical angles. c. converse of the corresponding angles theorem was used. d. m∠1 ≠ m∠3

Explanation:

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

• Option A: Corresponding angles are in the same relative position at each intersection. ∠2 and ∠3 do not have this relationship, so using them as corresponding angles is incorrect.
• Option B: Vertical angles are opposite each other when two lines intersect. ∠2 and ∠3 are not vertical angles, but this is not the core error here.
• Option C: The Converse of the Corresponding Angles Theorem requires corresponding angles to be congruent. Since ∠2 and ∠3 are not corresponding angles, the theorem’s converse was misapplied, but the primary error is misidentifying corresponding angles.
• Option D: ∠1 and ∠3 are vertical angles (so \( m\angle1 = m\angle3 \)), so this is false.

The student incorrectly assumed ∠2 and ∠3 are corresponding angles, which they are not.

Answer:

A. ∠2 and ∠3 are not corresponding angles.