Question

which segments are parallel?
select each correct answer.
□ \\(\overline{ab}\\)
□ \\(\overline{ef}\\)
□ \\(\overline{gh}\\)
□ \\(\overline{cd}\\)

Explanation:

Step1: Check $\overline{AB}$ and $\overline{EF}$

Angle at $A$ is $47^\circ$, angle at $E$ is $133^\circ$. $47^\circ + 133^\circ = 180^\circ$, so they are same - side interior angles supplementary. By the converse of same - side interior angles theorem, $\overline{AB}\parallel\overline{EF}$.

Step2: Check $\overline{EF}$ and $\overline{GH}$

Angle at $E$ is $133^\circ$, angle at $H$ is $133^\circ$. These are corresponding angles (assuming the transversal is the line containing $E - I - G$ and $F - I - H$). By the converse of corresponding angles theorem, $\overline{EF}\parallel\overline{GH}$.

Step3: Check $\overline{AB}$ and $\overline{CD}$ (not in options relation here)

Angle at $A$ is $47^\circ$, angle at $D$ is $34^\circ$, and $47^\circ+34^\circ
eq180^\circ$, so not parallel. Also, $\overline{GH}$ and $\overline{CD}$: angle at $H$ is $133^\circ$, angle at $D$ is $34^\circ$, $133^\circ + 34^\circ
eq180^\circ$, so not parallel.

Answer:

$\overline{AB}$ and $\overline{EF}$, $\overline{EF}$ and $\overline{GH}$