Question

eg and hj are parallel lines. which angles are corresponding angles? ∠efd and ∠jif ∠efd and ∠hif ∠efd and ∠hik ∠efd and ∠jik

Explanation:

To determine corresponding angles, we use the definition: when two parallel lines are cut by a transversal, corresponding angles are in the same relative position at each intersection. Here, \( \overleftrightarrow{EG} \) and \( \overleftrightarrow{HJ} \) are parallel, cut by transversal \( \overleftrightarrow{DK} \).

• \( \angle EFD \) is at the intersection of \( \overleftrightarrow{EG} \) and \( \overleftrightarrow{DK} \), below \( \overleftrightarrow{EG} \) and to the right of \( \overleftrightarrow{DK} \).
• \( \angle JIK \) is at the intersection of \( \overleftrightarrow{HJ} \) and \( \overleftrightarrow{DK} \), below \( \overleftrightarrow{HJ} \) and to the right of \( \overleftrightarrow{DK} \).

This matches the relative position of corresponding angles. Other options:

• \( \angle JIF \): Position does not match.
• \( \angle HIF \): Position (above \( \overleftrightarrow{HJ} \)) does not match.
• \( \angle HIK \): Position (above \( \overleftrightarrow{HJ} \)) does not match.

Answer:

\( \angle EFD \) and \( \angle JIK \)