Question

select all the pairs of corresponding angles.
∠gfd and ∠jif ∠jik and ∠hif
∠efd and ∠hif ∠gfd and ∠efd

Explanation:

Step1: Recall Corresponding Angles Definition

Corresponding angles are equal when two parallel lines are cut by a transversal, and they occupy the same relative position at each intersection.

Step2: Analyze Each Pair

• $\angle GFD$ and $\angle JIF$: Lines $FG \parallel IJ$, transversal $DK$. $\angle GFD$ and $\angle JIF$ are in corresponding positions (above the parallel lines, same side of transversal), so they are corresponding angles.
• $\angle JIK$ and $\angle HIF$: These are vertical angles (opposite angles formed by intersecting lines), not corresponding angles.
• $\angle EFD$ and $\angle HIF$: Lines $FE \parallel HI$, transversal $DK$. $\angle EFD$ and $\angle HIF$ are in corresponding positions (below/above? Wait, $FE$ and $HI$ are parallel, transversal $DK$. $\angle EFD$ (at $F$) and $\angle HIF$ (at $I$) are corresponding (same relative position: left - side of transversal, above/below? Wait, $FE$ is left - going, $HI$ is left - going. Transversal $DK$ cuts them. $\angle EFD$ and $\angle HIF$: yes, corresponding.
• $\angle GFD$ and $\angle EFD$: These are adjacent angles forming a linear pair (supplementary), not corresponding angles.

Wait, correction: $\angle JIK$ and $\angle HIF$: $\angle JIK$ and $\angle HIF$: when lines $HJ$ and $IJ$? No, $HJ$ is a straight line? Wait, $HJ$ is a line with $H$, $I$, $J$? Wait, the lines are $FG \parallel IJ$ and $FE \parallel HI$ (since $FE$ and $HI$ are both left - directed, $FG$ and $IJ$ are right - directed). Transversal is $DK$.

So correct corresponding angle pairs:

• $\angle GFD$ and $\angle JIF$: Corresponding (parallel lines $FG \parallel IJ$, transversal $DK$)
• $\angle EFD$ and $\angle HIF$: Corresponding (parallel lines $FE \parallel HI$, transversal $DK$)

The pair $\angle JIK$ and $\angle HIF$: $\angle JIK$ and $\angle HIF$ are vertical angles (since $HJ$ and $DK$ intersect at $I$, $\angle JIK$ and $\angle HIF$ are vertical angles, so not corresponding. $\angle GFD$ and $\angle EFD$: adjacent, linear pair, not corresponding.

So the correct pairs are $\angle GFD$ and $\angle JIF$, $\angle EFD$ and $\angle HIF$.

Answer:

The correct pairs of corresponding angles are $\boldsymbol{\angle GFD}$ and $\boldsymbol{\angle JIF}$, $\boldsymbol{\angle EFD}$ and $\boldsymbol{\angle HIF}$. (If we consider the checkboxes, the incorrect ones are $\angle JIK$ and $\angle HIF$, $\angle GFD$ and $\angle EFD$; correct are $\angle GFD$ and $\angle JIF$, $\angle EFD$ and $\angle HIF$)