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QUESTION IMAGE

given: lines p and q are parallel and r is a transversal. prove: ∠2 ≅ ∠…

Question

given: lines p and q are parallel and r is a transversal. prove: ∠2 ≅ ∠7
diagram of lines p, q (parallel), transversal r creating angles 1,2,3,4 on p and 5,6,7,8 on q
statements | reasons
--- | ---

  1. ( p parallel q ), ( r ) is a transv. | 1. given
  2. a | 2. vert. ( angle )’s ( cong )
  3. b | 3. corr. ( angle )’s thm.
  4. ( angle 2 cong angle 7 ) | 4. transitive prop.

which statements could complete the proof?
a: dropdown
b: dropdown

Explanation:

Step1: Analyze Statement A (Reason: Vert. ∠’s ≅)

Vertical angles are congruent. Looking at the diagram, ∠2 and ∠3? No, wait, ∠2 and ∠3 are adjacent, but ∠2 and ∠4? No, wait, vertical angles with ∠2: ∠2 and ∠3? No, ∠1 and ∠3 are vertical? Wait, no, ∠2 and ∠3 are adjacent, ∠2 and ∠4? No, wait, the vertical angle of ∠2 would be... Wait, ∠2 and ∠3? No, let's see: when two lines intersect, vertical angles are opposite. So line r intersects line p, forming ∠1, ∠2, ∠3, ∠4. So ∠2 and ∠3? No, ∠1 and ∠3 are vertical, ∠2 and ∠4 are vertical? Wait, no, ∠1 and ∠3 are vertical (opposite), ∠2 and ∠4 are vertical? Wait, no, when two lines intersect, the vertical angles are opposite. So ∠1 and ∠3, ∠2 and ∠4? Wait, no, ∠1 and ∠3: if you have[SSE Completed, Client Connection Error][LLM SSE On Failure]

Answer:

Step1: Analyze Statement A (Reason: Vert. ∠’s ≅)

Vertical angles are congruent. Looking at the diagram, ∠2 and ∠3? No, wait, ∠2 and ∠3 are adjacent, but ∠2 and ∠4? No, wait, vertical angles with ∠2: ∠2 and ∠3? No, ∠1 and ∠3 are vertical? Wait, no, ∠2 and ∠3 are adjacent, ∠2 and ∠4? No, wait, the vertical angle of ∠2 would be... Wait, ∠2 and ∠3? No, let's see: when two lines intersect, vertical angles are opposite. So line r intersects line p, forming ∠1, ∠2, ∠3, ∠4. So ∠2 and ∠3? No, ∠1 and ∠3 are vertical, ∠2 and ∠4 are vertical? Wait, no, ∠1 and ∠3 are vertical (opposite), ∠2 and ∠4 are vertical? Wait, no, when two lines intersect, the vertical angles are opposite. So ∠1 and ∠3, ∠2 and ∠4? Wait, no, ∠1 and ∠3: if you have[SSE Completed, Client Connection Error][LLM SSE On Failure]