Question

etermining Parallel Lines Cut by a Transversal
Consider transversal t cutting lines p and q.

Transversal t crosses lines p and q to form 8 angles. Clockwise from top left, the angles are 1, 2, 4, 3; 5, 6, 8, 7.

Which statement allows Carmen to conclude that line p and line q are parallel?
∠2 ≅ ∠6
∠1≅ ∠4
m∠1 + m∠2 = 180°
m∠5 + m∠7 = 180°

Answer 1

∠2 ≅ ∠6

Reason: ∠2 and ∠6 are corresponding angles (they occupy the same position at the two intersections). If corresponding angles formed by a transversal are congruent, then the two lines are parallel.