Question

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

Explanation:

Step1: Recall the definition of alternate - interior angles

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

Step2: Analyze each option

• For \(\angle CDG\) and \(\angle HGD\): \(\angle CDG\) is not an interior angle between the two parallel lines \(CE\) and \(FH\) with respect to the transversal \(BI\).
• For \(\angle EDB\) and \(\angle HGI\): \(\angle EDB\) is an exterior angle (not between the two parallel lines \(CE\) and \(FH\)) and \(\angle HGI\) is also not in the correct position for alternate - interior angles.
• For \(\angle FGD\) and \(\angle CDB\): \(\angle FGD\) is not in the correct position (not between the two parallel lines \(CE\) and \(FH\) in the right orientation)
• For \(\angle CDB\) and \(\angle HGD\):
• Lines \(CE\parallel FH\) and \(BI\) is the transversal.
• \(\angle CDB\) and \(\angle HGD\) are non - adjacent, lie between \(CE\) and \(FH\), and on opposite sides of the transversal \(BI\).

So, the alternate - interior angles are \(\angle CDB\) and \(\angle HGD\).

Answer:

\(\angle CDB\) and \(\angle HGD\)