Question

ce and fh are parallel lines. which angles are alternate interior angles? ∠cdg and ∠hgd ∠fgd and ∠cdb ∠edb and ∠fgd ∠cdg and ∠edg

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent angles that lie between two parallel lines and on opposite sides of a transversal.

Step2: Analyze each option

• For \(\angle CDG\) and \(\angle HGD\):

Since \(\overleftrightarrow{CE}\parallel\overleftrightarrow{FH}\) and \(\overleftrightarrow{IB}\) is a transversal. \(\angle CDG\) and \(\angle HGD\) lie between the parallel lines \(\overleftrightarrow{CE}\) and \(\overleftrightarrow{FH}\) and on opposite sides of the transversal \(\overleftrightarrow{IB}\).

• For \(\angle FGD\) and \(\angle CDB\): \(\angle FGD\) is outside the region between the parallel lines (if we consider the standard parallel - line - transversal setup for the given parallel lines \(\overleftrightarrow{CE}\) and \(\overleftrightarrow{FH}\)), so they are not alternate interior angles.
• For \(\angle EDB\) and \(\angle FGD\): \(\angle EDB\) is not in the correct position (not between the two parallel lines in the relevant sense for the alternate - interior - angle definition with respect to \(\overleftrightarrow{CE}\) and \(\overleftrightarrow{FH}\))
• For \(\angle CDG\) and \(\angle EDG\): These two angles are adjacent (share a common side \(DG\)), so they are not alternate interior angles.

Answer:

\(\angle CDG\) and \(\angle HGD\)