Given: ac||bd , ab||cd, and ac _|_ cd
prove: ∠pcq is complementary to ∠abc.

proof: since ac _|_ cd m∠ocq = 90° by the definition of perpendicular lines. by angle addition, we can say m∠ocq = m∠ocp + m∠pcq. but since m∠ocq = 90°, m∠ocp + m∠pcq = 90° by the transitive property of equality. [missing step] by the definition of congruent angles, m∠ocp = m∠abc. this leads to m∠abc + m∠pcq = 90° by the transitive property of equality. so, based on the definition of complementary angles, ∠pcq is complementary to ∠abc. what is the missing step in the given proof?

a. ∠pqc and ∠acp are supplementary by the linear pair theorem.

b. for parallel lines cut by a transversal, corresponding angles are congruent, so ∠acb ≅ ∠pcq.

c. ∠ocp ≅ ∠bcd by the vertical angles theorem.

d. for parallel lines cut by a transversal, corresponding angles are congruent, so ∠ocp ≅ ∠abc.

e. for parallel lines cut by a transversal, corresponding angles are congruent, so ∠oca ≅ ∠cbd.