Question

df and gi are parallel lines.
select all the pairs of alternate interior angles.
∠ihe and ∠ghj ∠fec and ∠feh
∠ghe and ∠feh ∠deh and ∠ihe

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each pair

• For \(\angle IHE\) and \(\angle GHJ\): These are vertical angles, not alternate interior angles.
• For \(\angle FEC\) and \(\angle FEH\): These are adjacent angles, not alternate interior angles.
• For \(\angle GHE\) and \(\angle FEH\): Since \(\overleftrightarrow{DF}\parallel\overleftrightarrow{GI}\) and \(JC\) is the transversal, \(\angle GHE\) and \(\angle FEH\) lie between the parallel lines and on opposite sides of the transversal.
• For \(\angle DEH\) and \(\angle IHE\): Since \(\overleftrightarrow{DF}\parallel\overleftrightarrow{GI}\) and \(JC\) is the transversal, \(\angle DEH\) and \(\angle IHE\) lie between the parallel lines and on opposite sides of the transversal.

Answer:

\(\angle GHE\) and \(\angle FEH\), \(\angle DEH\) and \(\angle IHE\)