Question

given: $overleftrightarrow{nc}paralleloverleftrightarrow{bg}$ and $angle hrscongangle hts$ prove: $overleftrightarrow{dk}paralleloverleftrightarrow{mw}$ a partially - completed two - column proof is shown.

step	statements	reasons
2	$angle hrs$ and $angle rht$ are supplementary	if two parallel lines are intersected by a transversal, then consecutive interior angles are supplementary
3	$mangle hrs + mangle rht=180^{circ}$	definition of supplementary angles
4	$mangle hrs = mangle hts$	definition of congruence
5	$mangle hts + mangle rht=180^{circ}$	substitution property of equality
6	$angle hts$ and $angle rht$ are supplementary	definition of supplementary angles
7	$overleftrightarrow{dk}paralleloverleftrightarrow{mw}$

which of the following reasons can be used to justify step 7?
if two parallel lines are intersected by a transversal, then alternate interior angles are congruent.
if two parallel lines are intersected by a transversal, then consecutive interior angles are supplementary.
if two lines are intersected by a transversal so that alternate interior angles are congruent, then the lines are parallel.
if two lines are intersected by a transversal so that consecutive interior angles are supplementary then the lines are parallel.

Explanation:

In step 6, we have shown that $\angle HTS$ and $\angle RHT$ are supplementary. These are consecutive - interior angles formed by lines $\overrightarrow{DK}$ and $\overrightarrow{MW}$ with a transversal. By the converse of the consecutive - interior angles postulate, if two lines are intersected by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.

Answer:

If two lines are intersected by a transversal so that consecutive interior angles are supplementary then the lines are parallel.