Question

which segments are parallel? select each correct answer. ef cd ab gh

Explanation:

Step1: Analyze \( \overline{EF} \) and \( \overline{GH} \)

Check the angles formed with the transversal. The angle at \( E \) is \( 133^\circ \), and the angle at \( H \) is also \( 133^\circ \). These are corresponding angles (or same - side interior angles supplementary? Wait, \( 180 - 133 = 47 \), but here the equal angles suggest \( \overline{EF} \parallel \overline{GH} \) by corresponding angles (if the transversal is the line through \( I \)).

Step2: Analyze \( \overline{AB} \) and \( \overline{CD} \)

In triangle \( ABD \) (or the figure with \( A,B \) and \( C,D \)), the angle at \( A \) is \( 47^\circ \), and the angle at \( D \) is \( 34^\circ \)? Wait, no, let's recalculate. Wait, the angle adjacent to \( 133^\circ \) at \( E \) is \( 180 - 133 = 47^\circ \), which is equal to the angle at \( A \). So \( \overline{AB} \parallel \overline{CD} \) by corresponding angles (since the transversal creates equal corresponding angles: \( 47^\circ \) at \( A \) and the angle adjacent to \( 133^\circ \) at \( E \), and also the angle at \( D \) and the other angle? Wait, maybe better to see:
For \( \overline{AB} \) and \( \overline{CD} \): The angle at \( A \) is \( 47^\circ \), and if we look at the angle related to \( CD \), the angle at \( D \) is \( 34^\circ \)? No, wait, maybe I made a mistake. Wait, the key is:

• \( \overline{EF} \) and \( \overline{GH} \): The \( 133^\circ \) angles are equal, so they are parallel (corresponding angles).
• \( \overline{AB} \) and \( \overline{CD} \): The angle at \( A \) is \( 47^\circ \), and the angle that is supplementary to \( 133^\circ \) is \( 47^\circ \), and the angle at \( D \) - wait, maybe the correct pairs are \( \overline{AB} \parallel \overline{CD} \) (by alternate interior angles or corresponding angles) and \( \overline{EF} \parallel \overline{GH} \).

Wait, let's re - examine:

• For \( \overline{EF} \) and \( \overline{GH} \): The transversal is the line passing through the intersection point \( I \). The angle at \( E \) (between \( \overline{EF} \) and the transversal) is \( 133^\circ \), and the angle at \( H \) (between \( \overline{GH} \) and the transversal) is also \( 133^\circ \). So by the converse of the corresponding angles theorem, \( \overline{EF} \parallel \overline{GH} \).
• For \( \overline{AB} \) and \( \overline{CD} \): The angle at \( A \) is \( 47^\circ \), and the angle adjacent to \( 133^\circ \) at \( E \) is \( 180 - 133 = 47^\circ \). Also, if we consider the other transversal, the angle at \( D \) and the angle related to \( AB \) should be equal. So \( \overline{AB} \parallel \overline{CD} \).

Answer:

The correct segments that are parallel are \( \overline{EF} \), \( \overline{GH} \), \( \overline{AB} \), \( \overline{CD} \) (so we select the checkboxes for \( \overline{EF} \), \( \overline{CD} \), \( \overline{AB} \), \( \overline{GH} \)).