eg and hj are parallel lines. select all the pairs of alternate interior angles. ∠hif and ∠efd ∠gfi and ∠hif ∠hif and ∠jik ∠efd and ∠jif

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Accepted Answer

# 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 $\angle HIF$ and $\angle EFD$:
  - Transversal $KD$ crosses parallel lines $HJ$ and $EG$.
  - $\angle HIF$ and $\angle EFD$ lie between $HJ$ and $EG$ and on opposite sides of $KD$. So they are alternate interior angles.
- For $\angle GFI$ and $\angle HIF$:
  - Transversal $KD$ crosses parallel lines $HJ$ and $EG$.
  - $\angle GFI$ and $\angle HIF$ lie between $HJ$ and $EG$ and on opposite sides of $KD$. So they are alternate interior angles.
- For $\angle HIF$ and $\angle JIK$:
  - These are vertical angles (opposite angles formed by the intersection of two lines $KD$ and $HJ$), not alternate interior angles.
- For $\angle EFD$ and $\angle JIF$:
  - Transversal $KD$ crosses parallel lines $HJ$ and $EG$.
  - $\angle EFD$ and $\angle JIF$ lie between $HJ$ and $EG$ and on opposite sides of $KD$. So they are alternate interior angles.

# Answer:
$\angle HIF$ and $\angle EFD$, $\angle GFI$ and $\angle HIF$, $\angle EFD$ and $\angle JIF$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the definition of alternate interior angles

Step2: Analyze each pair

Answer: