Question

in the given figure, which lines or segments are parallel? justify your answer.

choose the correct answer below

○ a. $overleftrightarrow{eq} parallel overleftrightarrow{ab}$ by the converse of the alternate exterior angles theorem

○ b. $overleftrightarrow{eq} parallel overleftrightarrow{ea}$ by the converse of the corresponding angles theorem

○ c. $overline{ea} parallel overline{bc}$ by the converse of the same-side interior angles postulate

○ d. $overleftrightarrow{ab} parallel overline{bc}$ by the converse of the alternate interior angles theorem

Explanation:

To determine parallel lines, we analyze each option:

• Option A: $\overleftrightarrow{EQ} \parallel \overleftrightarrow{AB}$ – Not supported by the diagram's angle relationships.
• Option B: $\overleftrightarrow{EQ} \parallel \overleftrightarrow{EA}$ – These are perpendicular (from the diagram's right angles), so not parallel.
• Option C: $\overline{EA} \parallel \overline{BC}$ – $\overline{EA}$ and $\overline{BC}$ are both vertical (right angles with horizontal lines), so by Converse of Same - Side Interior Angles Postulate (or recognizing right angles imply parallelism), this holds.
• Option D: $\overleftrightarrow{AB} \parallel \overline{BC}$ – $\overleftrightarrow{AB}$ is horizontal and $\overline{BC}$ is vertical, so they are perpendicular, not parallel.

Answer:

C. $\overline{EA}\parallel\overline{BC}$ by the Converse of the Same - Side Interior Angles Postulate