Question

practice
example 1
use the given information to determine which lines, if any, are
parallel. state the postulate or theorem that justifies your answer.

1. ( angle 3 cong angle 7 )
2. ( angle 9 cong angle 11 )
3. ( angle 2 cong angle 16 )
4. ( m angle 5 + m angle 12 = 180 ^ { circ } )

given the following information, determine which lines, if any, are
parallel. state the theorem that justifies your answer.

1. ( angle 1 cong angle 6 )
2. ( m angle 7 + m angle 6 = 180 ^ { circ } )

Explanation:

Step1: Identify the relationship between ∠1 and ∠6

∠1 and ∠6 are alternate exterior angles.

Step2: Apply the Alternate Exterior Angles Theorem

If alternate exterior angles are congruent, then the lines are parallel. Since ∠1 ≅ ∠6, by the Alternate Exterior Angles Theorem, lines \( p \) and \( q \) are parallel.

Answer:

Lines \( p \) and \( q \) are parallel by the Alternate Exterior Angles Theorem.