Question

question 10 (5 points) listen which of the following statements must be true to prove that lines p and q are parallel? a) ∠2 ≅ ∠7 b) ∠4 ≅ ∠6 c) ∠1 ≅ ∠7 d) ∠1 ≅ ∠4

Explanation:

To prove lines \( p \) and \( q \) are parallel, we use angle - related postulates (e.g., Alternate Interior Angles Theorem).

• For option A: $\angle 2$ and $\angle 7$ are not a standard pair (corresponding, alternate interior, etc.) to prove parallelism.
• For option B: $\angle 4$ and $\angle 6$ are alternate interior angles. By the Alternate Interior Angles Theorem, if alternate interior angles are congruent, then the two lines cut by a transversal are parallel. So if $\angle 4\cong\angle 6$, lines \( p \) and \( q \) (cut by the transversal) are parallel.
• For option C: $\angle 1$ and $\angle 7$ do not form a pair that can be used to prove \( p\parallel q \) using standard parallel - line angle postulates.
• For option D: $\angle 1$ and $\angle 4$ are vertical angles (always congruent), but this does not prove \( p\parallel q \).

Answer:

B. $\angle 4 \cong \angle 6$