Question

b unit 7 task 04
is two-column proof shows that $overleftrightarrow{ac}\parallel\overleftrightarrow{bd}$ in the attached diagram, but it is incomplete.
select the correct reason to complete the proof.
a. $\angle abd$ and $\angle bdc$ are supplementary; corresponding angles theorem
b. $\angle abd\cong\angle bdc$; corresponding angles theorem
c. $\angle abd\cong\angle bdc$; consecutive interior angles theorem
d. $\angle abd$ and $\angle bdc$ are supplementary; consecutive interior angles theorem

Explanation:

To prove $\overleftrightarrow{AC} \parallel \overleftrightarrow{BD}$, we use the converse of the consecutive interior angles theorem: if two lines are cut by a transversal and consecutive interior angles are supplementary, the lines are parallel. $\angle ABD$ and $\angle BDC$ are consecutive interior angles for transversal $BD$ cutting $\overleftrightarrow{AC}$ and $\overleftrightarrow{BD}$. The consecutive interior angles theorem (or its converse) applies to their supplementary relationship.

Answer:

D. $\angle ABD$ and $\angle BDC$ are supplementary, Consecutive interior angles theorem