Question

Letters a, b, c, and d are angles measures.

Lines m and n are cut by transversal p. At the intersection of lines p and m, labeled clockwise, from uppercase left, the angles are: a, b, c, blank. At the intersection of lines p and n, labeled clockwise, from uppercase left, the angles are: blank, blank, d, blank.

Which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? Select three options.

a = c
a = d
c = d
b + c = 180°
b + d = 180°

Answer 1

Answers: a = d, c = d, and b + d = 180°.

Reasons:
- a = d: a and d are alternate exterior angles; equality of alternate exterior angles implies the lines are parallel.
- c = d: c and d are corresponding angles; equality of corresponding angles implies the lines are parallel.
- b + d = 180°: since b + c = 180° (linear pair at the top intersection), b + d = 180° implies c = d, which is the corresponding-angles condition and thus implies the lines are parallel.

a = c and b + c = 180° are only facts about one intersection (vertical angles or a linear pair) and do not prove the two lines are parallel.