Question

question 1-2 in the diagram, ∠gde and ∠def are supplementary. which lines are parallel? de || gf dg || ef de || ef neither pair of lines is parallel

Explanation:

Step1: Recall parallel - line theorem

If two lines are cut by a transversal and a pair of same - side interior angles are supplementary, then the two lines are parallel.

Step2: Identify same - side interior angles

In the diagram, \(\angle GDE\) and \(\angle DEF\) are same - side interior angles formed by the transversal \(DE\) and lines \(\overleftrightarrow{DG}\) and \(\overleftrightarrow{EF}\).

Step3: Apply the theorem

Since \(\angle GDE\) and \(\angle DEF\) are supplementary, by the same - side interior angles postulate, \(\overleftrightarrow{DG}\parallel\overleftrightarrow{EF}\).

Answer:

\(\overleftrightarrow{DG}\parallel\overleftrightarrow{EF}\) (corresponding to the option \(\overleftrightarrow{DG}\parallel\overleftrightarrow{EF}\) in the multiple - choice list)